No problem .
When my children were small all I really needed was notice if my childcare arrangement were going to be disrupted. I had cover from when I left the house in the morning until 6.30pm, which was usually enough, but occasionally meetings would be called without a finish time, and that made things really difficult. I didn't (and still don't) think it unreasonable for there to be a policy of agreeing that late meetings should have an end time unless the workplace is dealing with emergencies that won't wait. It used to make me twitch when someone suggested breaking for coffee half way through! If a meeting was likely to be going to run late, even a day's notice would have allowed me to make plans to extend my childcare.
When it comes to holidays, in my experience people without children are far less likely to want time off in August or at Easter, when everything is a lot busier and more expensive. They usually preferred to avoid other people's children.
Christmas is a time when most people want to be with family, whether or not they have children, so I don't think it's fair for parents to always take priority. Easter is less of an issue, as the religious side happens at the weekend, and the rest of the school holidays are not in high season, so I can't imagine lots of people would want to take leave then, but if they do, then again, I think it should be done on a rota system.
Basically, where policies can be put in place so that everyone can have a work/life balance, they should be. Occasional cover for things like sickness is a fact of life, but I can honestly say that I don't remember ever taking time off because of my children (my husband and I somehow managed to juggle things between us), but I regularly got 'dropped in it' by a (child-free) colleague who took sick leave every time she felt stressed, which was at least once a month - it's not a one-way street.