How would you split the cost of this trip?

I think between a family it's a bit more about ability to pay.

If you are a not very well off single person being asked to pay half by your much wealthier, married sibling, then that is not nice. If you are a struggling SAHP with a disabled teen and your single sibling is a hotshot venture capitalist then it's not nice if they are expecting you to pay half. Whether the other parent should chip in depends on whose idea it was and everyone's relative ability to pay too. Fair doesn't always mean equal.

Yes this sounds fair

OP; I’m going to put it out there that this isn’t a trip you will enjoy

This

The teen will likely eat just as much as the adults too - though presumably not drink? - so that'll need splitting per person too, and of course the parents are free to pay for their own teen if they wish

From you saying it was a surprise.

Kids pay for themselves and their spice and kids (if they have them)

Your household takes care of your and the birthday parent's flights.

By bedroom 🤷‍♀️ for cost of lodgings.
Any other cost by person.

It depends how petty you want to be. If 2 siblings have planned a holiday as a gift for a parent it should be 50/50 between them. Otherwise I agree with @Kindafreakingouthere If you’re looking at a cost per head, then the single person should pay a third and the other 2/3. Assuming a cost of eg £1200, that’s £200 pp so you pay for your own household and half of your parents. I wouldn’t expect the other parent to contribute

I 100% agree with this. It feels fair and it also equates with rooms on the basis that the family will be occupying 2 rooms.

I really hope this is not another one of these couple-with-a-child-trying-to-get-subsidised scenarios!

Divide the total by 6 to get the cost per person.
other parent pays for 1 person plus 1/3 of birthday parent
2 adults and teen pay for 3 people plus 1/3 of birthday parent
Single person pays for 1 person plus 1/3 of birthday parent

Whose idea was it?
What actual costs are involved? (Accommodation only? Flights? Etc)
Which one are you in this situation?

Divide the total (£600) by the amount of people going - including the teen. Each group pays their own i.e the other parent pays 1/6 (£100), the family of 3 pay 3/6 (£300) and the singleton pays 1/6 (£100). The remaining 1/6 (£100) for the birthday parent should then be split equally between the 3 groups (£33). I can’t see how it would be split any other way.
Other parent - £133
Family of 3 - £333
Singleton - £133

Divide by either 4, or 4.5 ( if you want to include the teen, count them as a half)

We split the cost by rooms. If “parents” are in one room we’d cover the cost of that room, if it’s a gift. Same way if the parents who gift it was, was single we’d cover the costs

If other parts of the family require more rooms, as they have more children then they pay for that room. I.e. parents plus two children = 2 rooms that they pay for. If they’re happy all being one one room they pay for a room

Single person has a room and pays for a room

I think it depends on whose idea it was and how it was pitched. If the adult children have said ‘we want to treat mum’ I sort of think they should be covering the costs for the room for the mum and dad. If the idea came from the Dad as a ‘oh wouldn’t it be nice for us all to get together’ then I think he should be contributing too.

I think number of rooms is also a factor. Im
assuming 4 rooms.

So assuming cost is £1000

in scenario 1

Single child: £375
child with husband and teen: £625

in scenario 2

Dad: £250
Child 1: £250
family: £500

In some families, they might be willing to adjust to split the additional costs of the teen more evenly across so something like below.

Dad: £300
child 1£300
family £400

This. As a divorced adult it does piss me off to always be expected to be happy to pay the same for a small single room or sofa bed in the lounge as couples on 2 incomes getting the nice big room with en suite!

so divide costs by 5
birthday parent goes free
other parent and single adult pay 1/5 each
married couple with teen pay 3/5 (1/5 each)

I don’t think you have posted the number of bedrooms anywhere, but to me that’s the fairest split. Unless teen is in a box room or small single in which case it comes across as a bit mean to charge for a whole room.
However for the sake of family harmony I would probably suck up an even split.

Split it by bedrooms.

If the non birthday parent is very well off then maybe 25/25/50% (the family) but if not then would say a third/two thirds split as would be a nice gesture to treat the parents and maybe the non birthday parent could then pay for a meal out?

It really does mean that. There is a big difference between me and my husband discussing and agreeing that spending money on each other is fine, and jointly deciding how much, and having a (potentially significant) expenditure sprung on me without discussion.

Every single reply has been just one sentence, so people are having to ask question after question. If you explain the situation, people are more like it to be able to give you relevant answers!