Hello Judy, Here is Richard's obituary. It may give you some info you don't already have?

The death occurred on Saturday of Mr. Richard Joseph Waldron at his residence, Wattle-street, at the age of 73 years. The deceased gentleman was a native of Galway, Ireland. He came to Australia in 1863, but before settling down he toured New Zealand, Queensland, and New South Wales. Arriving in Melbourne, he journeyed to Bendigo, and entering the service of the Education department, he taught in schools at Bendigo and Ballarat for some years. Severing his connection with the department, the late Mr. Waldron opened a grocer's shop at Kangaroo Flat. Whilst conducting this business he also had some cabs plying for hire in the city, and after a while he relinquished the grocery trade and commenced driving a cab himself. This he continued to do for about 40 years, and at the time of his death he was the oldest cabdriver in Bendigo. About 10 months ago the deceased gentleman met with a slight accident whilst following his occupation, from the effects of which he never fully recovered, and the shock, coupled with a general break-up of the system, was responsible for his death. The late Mr. Waldron was highly esteemed by a wide circle of friends, who will regret to hear of his demise. Some 46 years ago he married Miss Foley, a native of Ireland, who survives him. A family of three sons and one daughter is also left. The sons are Mr. J. Waldron (of West Australia), Mr. T. Waldron (who conducts a wine cafe in View-street), and Mr. W. Waldron (wine merchant, of Bull-street). Miss Waldron resides at home. In accordance with the deceased gentleman's wish, he was buried privately in the Bendigo Cemetery yesterday, a goodly number of sympathising friends joining the cortege. The pall-bearers were Messrs. J. Commons, D. Duffy, J. McGinley and W. Hayes. The burial service was solemnised by the Rev. Father Heffernan. Mr. T. Sayer, of Bridge-street, conducted the mortuary arrangements. Several beautiful floral tributes were received.
Bendigo Advertiser (Vic. : 1855 - 1918), Monday 29 April 1912, page 8

According to Vic BDM Catherine Waldron died at Bendigo in 1919 aged 75. Her mother is recorded as Margaret Oates and her father is John Foley.

The Bendigo Cemetery records show Catherine died 27 August 1919. On the headstone there is Richard's name and also two other names

- Rose Ann Waldron died 5 Feb 1948 aged 73 - her parents are Catherine Foley and Richard Waldron. BDM has her name as Roseanne Jane, born Kangaroo Flats

-Alma Waldron, died 30 Nov 1989 aged 84. Her mother is Nora Mary Fitzgerald and father is Thomas Richard Waldron. (Richard and Catherine's son)

Thomas Richard Waldron is buried at the Bendigo Public Cemetery. He died 26 January 1952 aged 75 years. His parents are Catherine Foley and Richard Waldron.

William Ferdinand Waldron died in Vic in 1953 aged 73, born in Bendigo. His parents are also Catherine Foley and Richard Waldron.

Michael John Waldron died in Subiaco, WA, in 1927 aged 57. His parents are Catherine Foley and Richard Waldron.

Here's a bit more - this should fill in a few gaps for you and your mother :)

OBITUARY THE LATE MR. MICHAEL JOHN WALDRON. The death of the late Mr. Michael John Waldron, of 24 Harley-street, Highgate Hill, occurred at St. John of God Hospital Subiaco, on May 30, after one week's illness. The deceased, who was born in Bendigo, Victoria, 57 years ago, had been a resident of this State for the past 25 years, and for practically the whole of that time had been an employee of Messrs. Foy and Gibson Pty. Ltd. His was a well-known figure in the grocery section of their establishment, and one that will be missed by not only the members of the staff, but, by the many friends and business acquaintances he had made with his genial and obliging disposition. The respect and esteem in which the deceased was held was evidenced by the unusually large and re-presentative gathering at the graveside and by the many beautiful floral tributes as well as the numerous letters of condolence which were received. A Requiem Mass was celebrated at 9 o'clock in the morning of May 31 at the Sacred Heart Church, Highgate Hill, and in the afternoon the funeral cortege moved from there to the Roman Catholic portion of the Karrakatta Cemetery. The chief mourners were Mrs. J. Waldron (widow), Misses Monica, Kathleen, and Irene Waldron (daughters), and Messrs. John and Joseph Waldron (sons). The pall-bearers were Messrs. C. Helm. T. Joyce, H. Levy, W. Lees, A. Pownall, and C. Gallus. The funeral arrangements were carried carried out by Bowra and O'Dea.
Daily News (Perth, WA : 1882 - 1955), Monday 13 June 1927, page 8

WALDRON. — On May 30, 1927, at the St. John of God Hospital, Subiaco, Michael John, the beloved husband of Johanna Waldron, of 24 Harley-street, Highgate Hill, and fond father of Monica, Kathleen, Irene, John, and Joseph Waldron, aged 57 years. R.I.P.

Michael John Waldron married Johanna McInerney in 1898 in Victoria.
BDM Vic 569 / 1898
Their children are
John Francis Waldron born 1898 in Bendigo, Victoria 24270 / 1898
Irene Josephine Waldron born 1908 in Perth, WA 100999
Joseph Richard Waldron born 1910 in Perth, WA. 101223

I haven't been able to find Monica or Kathleen's birth records.

WALDRON.-On February 7, 1944, Johanna, dearly loved wife of the late Michael John Waldron, beloved mother of John, Monica (Sister Mary Theodoret, Sacred Heart Convent Highgate), Kathleen, Irene (Mrs R. Graham) and Joe; beloved sister of Bridget Mclnerney; fond mother-in-law of Lily and Bob, and loved grandmother of John. Nola, Frank and Michael. Requiescat in pace.
West Australian (Perth, WA : 1879 - 1954), Tuesday 8 February 1944, page 1

WALDRON.-On February 7. 1944, at Mt Lawley, Johanna, dearly loved mother and mother-in-law of Rene and Bob Graham and darling Nanna of Nola and Michael.

GRAHAM-WALDRON.— on June 7, at the Sacred Heart Church Highgate, Joseph Robert. eldest son of Mr and Mrs. J J Graham (Kondinin) to Irene Josephine, youngest daughter of Mrs J Waldron and the late Mr J Waldron of Perth,
West Australian (Perth, WA : 1879 - 1954), Monday 5 July 1937, page 1


WALDRON - BROWN.

On Saturday evening, January 5. the Sacred Heart Church, Highgate, was artistically decorated for the marriage of Lilian, eldest daughter of Mr and Mrs Arthur Brown, of Vincent street, Mt. Lawley, and John Francis, son of Mrs. J. Waldron and the late Mr. John Waldron, of Mt. Lawley, which was solemnised by the Rev. Father Crowley. The bride, who was given away by her father, wore a lovely frock of soft ivory satin, the skirt being finished with a transparent hem heavily embroidered with silver and studded with rhinestones. The tightfitting bodice was relieved with palest pink georgette front with girdle of rhinestones at waist The veil of Brussels lace fell gracefully to form a train
and a sheaf of Madonna lilies, tied with a bow of white satin ribbon, completed a charming toilette. Miss Marjorie Brown (sister of the bride), and Miss Kathleen Waldron (sister of the bridegroom) were the bridesmaids. Miss Brown wore pin-tucked ivory georgette, featuring the hip yoke and flared skirt. A picture hat and bouquet of pale mauve and pink completed her toilette. Miss Waldron was gowned in ivory georgette, relieved with touches of blue and lemon, and wore a picture hat edged with tulle. She carried a bouquet to tone. Mr. Tom Bogue acted as best man and Mr. Laurie M'Comish was groomsman. During the signing of the register. Miss Kitty Brown, sister of the bride gave a charming rendering of Hoben's "Ave Maria." After the ceremony Mr and Mrs. Brown held a reception at the Oxford, Mt. Lawley. Mrs. Brown received her guests in a gown of silver grey crepe de chine, with hat en suite. She carried a bouquet of gold roses. Mrs. Waldron mother of the bridegroom, was becomingly gowned in black with hat to tone. During the wedding repast the usual toasts were honored. The bride and bridegroom left for their honeymoon during the evening the bride wearing a frock of hydrangea blue crepe mystic and coat and hat of grey to match. The happy couple were the recipients of many beautiful presents.
Sunday Times (Perth, WA : 1902 - 1954), Sunday 27 January 1929, page 3

WALDRON: On March 29, at Subiaco, Sister Mary St. Theodoret, of Convent Notre Dame Des Missions, Maylands, daughter of the late Mr. and Mrs. John Waldron, loving sister of John (Melbourne), Kathleen, lrene and Joseph.
WALDRON: On March 29, 1948. Sister Mary St. Theodoret, of The Sacred Heart Convent, Highgate Hill.
West Australian (Perth, WA : 1879 - 1954), Tuesday 30 March 1948, page 1

MclNERNEY: On July 13. Bridget McInerney, of 24 Harley street, Highgate, beloved aunt of Jack (Melbourne), Kathleen, Irene, and Joseph Waldron. Requiescat in pace.
West Australian (Perth, WA : 1879 - 1954), Saturday 14 July 1951, page 23

WALDRON-PATRICK.- On February 11, at Sacred Heart Church, Highgate. Joseph, youngest son of the late Mr. and Mrs Waldron of Highgate to Ella, second daughter of Mr. and the late Mrs. Patrick, of South Perth.
West Australian (Perth, WA : 1879 - 1954), Thursday 7 March 1946, page 1

WALDRON: On January 19, at Hawthorn Hospital. to Ella and Joe -a son. Both well.
West Australian (Perth, WA : 1879 - 1954), Saturday 31 January 1948, page 1