Do parents of young children get any kind of priority with regards to taking AL during school holidays or is it fairly random have you found?
The way rostered leave works is through a pattern often called a 'rotation'.
The rotation might look something like (as a random example): 3 - 10 - 5 - 13 - 2 - 8 - 1 - 7 - 4 - 11 - 6 - 12 - 9.
The various weeks of block leave all have a number, e.g. Period 1, Period 2, Period 3 and so on.
The blocks will likely vary between train operating companies, but where I am your four weeks leave is divided into three blocks - a week 'Spring', two weeks 'Summer' and a week 'Winter' (there is no autumn due to the Summer slots being two weeks long). These might typically fall something like Spring (Feb-Apr), Summer (May-Oct) and Winter (Nov-Jan).
So say you were Period 3. You may be allocated one week in February, two weeks in May and one week in November.
The following year you will be Period 10 in the example rotation above, so you may be allocated one week in April, one week in October, and one week in January.
Then the third year you'll be Period 5 dates, fourth year Period 13 dates, and so on.
Those with kids therefore don't get priority as it's all done fairly in such a way that everyone gets their fair share of the 'good' dates (height of summer months) and the generally less desired ones (two weeks summer leave at start of May or end of October, for example). It wouldn't really be fair for some people to have to have all of their holidays at less favourable times just because they don't/can't have children. That said, you can always approach someone with school holiday dates and see if they'd be up for swapping, for example because they don't have kids and their partner isn't a teacher. But because those people are in demand, they will often be inundated with offers so will naturally likely help their mates or choose a swap proposal from someone with dates that suit their needs. For example, when I didn't have kids but had school holidays allocated, I would generally swap with someone offering me two weeks Summer leave in September (when the weather is nice but kids back at school) over someone offering me two weeks Summer leave at start of May or end of October.
When it comes to your remaining ad-hoc days (sometimes called 'floating days'), then this is very much first come first served. There will be a quota of how many people can be off each day to ensure there's enough staff still in to cover the train service, so say that quota allows 5 people to be ad-hoc each day, the first 5 people to book it will get it. Some operators may have a waiting list and agreement that they'll grant you the leave if there is a rest day volunteer worker who can do your shift, but you'll often only find this out two days before which isn't always much use depending what you want the day off for.
Note also that at some operators they will make you use 2 of your ad-hoc days on Christmas Day and Boxing Day, even though they don't run any trains so you couldn't even work if you wanted to. Some operators let you move rest days that week though, so if you were due to work 25th/26th December, you could move your (for example) 23rd/24th rest days to the 25th/26th, and you work 23rd/24th instead.