If he is reasonable he should come to some agreement
Exactly nanna8. If the child lived in the UK then either parent with parental responsibility can take their child on holiday for up to a month. That is the law here but I don’t know the law in Australia. And indeed many families are are able to come to arrangements perfectly amicably about holidays and the father will take the child away for a holiday and another time the mother will take the child away on holiday. Perfectly reasonably. But this father is exercising control over the mother primarily. Many ex husbands do this and some ex wives do it too.
The best thing this family can do it seems to me, is holiday in the mother’s home town, or very close to it. Then the grandparents can spend time with their daughter and also their grandchild, on the days they’re allowed.