I don't think Elizabeth was married to Bertie's father... unless he was named McKenzie also
This is what I have dug up including supporting information:Birth:
MCKENZIE ELIZABETH b. 1856 PATRICKS PLAINS #7014
Parents: ANDREW & SUSANNAH
Marriage:
MCKENZIE BESSIE m.
DUGGAN MICHAEL 1897 MUSWELLBROOK #1465
Death:
DUGGAN ELIZABETH KATHLEEN d. 1951 MUSWELLBROOK #18910
Parents: ANDREW & SUSAN
Obit:
http://trove.nla.gov.au/ndp/del/article/82759626Mrs. Elizabeth Duggan
The death recently of Mrs. Elizabeth Kathleen Duggan removed from Denman its oldest member of the community. Deceased, who was 95 years of age was familiarly known as "Grandma." She was born at Jerry's Plains, and for many years resided with her husband on their property at Hollydene, but since his passing about 10 years ago she went to Denman and for the past six years had resided with her son and daughter-in-law, Mr. and Mrs. Bert McKenzie, a floral tribute from them and daughter, Fay, being placed on the casket, mounted on her prized possesion, a feathered fan, which deceased had carried to the many dances and balls she had attended over 75 years ago. Deceased is survived by two sons, Mr. Bert McKenzie and Mr. Jack Duggan. The interment took place in the Church of England portion of the Muswellbrook cemetery. Rev. J. B. Neville officiated. Pall-bearers were Messrs. Norman and Milton Durham, Victor and Allan Oakes.Milton Durham one of the Pall-bearers was Bertie's second wife's (Hilda May DURHAM) brother

Bertie had a half brother John also known as Jack:
DUGGAN JOHN b. 1897 MUSWELLBROOK #14472
Parents: MICHAEL & BESSIE
Michael's death:
DUGGAN MICHAEL d. 1938 MUSWELLBROOK #18472
Parents: MICHAEL & CATHERINE