This is all about friendship and not about totting up the cost and gifting to replicate the coat, or the need to reciprocate a holiday to the same value.
A bunch of flowers is a nice thank-you.
An offer of a day out with your family or to join you on a camping holiday is something nice if it fits well with what your family might be doing, an extra child would be a positive rather than a burden and if you would all enjoy it. It isn't essnrtial by any means. And the fact that your holiday might be camping rather than staying in an owned property, or cost more or less than what your DD was taken on is neither here nor there ...its just about the friendship of the girls and the continuing relationship. Families invite other children to what they have already planned and what their family enjoy....any guest just fits in, whether that's ultimate luxury or extreme basics.
When we have take a friend, it has usually been self catering. There is always an extra bed so the accommodation doesn't cost us extra. It is within the UK, so no extra travel costs. It does cost us for the extra meal out each evening and an extra entrance fee or activity fee each time. But we are happy with that or we wouldn't invite the friend. Our own children get a lot of pleasure from the friend and we enjoy the extra company too.
We once did invite my brothers children to come skiing with us. The invitation was made on the basis of them paying for their kids' flights and ski costs, although we were covering the accommodation. In the end Covid put paid to that happening, but my brother was really happy with the arrangement....he wasn't available to take the kids skiing and was really grateful to us for including them. The conversation about costs happened at the same time as the invitation. If it had been a friend for that kind of holiday with those costs, we would have offered something similar. They are always welcome to accept or decline. Either is fine.
My DD was invited to go away with a school friend, along with a couple of others too. This would have involved a short flight and staying at the property owned by the friends family. Each friends family were to pay the flight cost (suggested flights from host, but left to individuals to book) and the costs of the holiday were to be funded by the hosts. Gifts of choc/wine/biscuits were given by families at the start (rather like you might if involved with an Exchange) and again a couple gave similar at the end.
Hosting another child on holiday does cost. It might not cost much extra than the family costs, if self catering and eating in and not doing many activities, but there will be some costs, even if it's the odd ice cream. I think you have to expect to incur those costs if you invite a child to join you. And you choose your form of eating and type of activities based on what you're prepared to pay for.....fine to do luxurious expensive activities every day if you're happy to pay. It doesn't really work if you're not.
The kid of holiday where you pay extra for accommodation for an extra person, such as extra flights, extra hotel room, extra ski pass, extra ski lessons is probably less suited to taking an extra along, for all but the very well off. Where an extra adds a couple of grand to the overall cost before you even arrive, most people won't want to do that, but some will.
It's always good to have a conversation about costs before anything is agreed to avoid misunderstandings. Too many threads on MN are about someone having accepted an invitation without this conversation....they hadn't been to,f it would involve a contribution and later found out it would when it was too,late to pull out......cue lots of grievance. Or other threads about those taking a kid who had expected a contribution but hadn't said and now feel lots of angst about a family not contributing. As long as people make things clear up front, anyone is free to accept or decline an invitation in full receipt of the knowledge of any costs it might incur (or not) for them. And it doesn't have to be awkward. '
We are going on holiday to X and would love Mary to join us if she's able to. We've booked a cottage and Jane's bedroom will have 2 beds, so plenty of room for Mary. We will be very happy to include Mary in everything we are doing for the week, but she might just like to bring some pocket money in case she wants to buy a souvenir etc'
Or
'We are going to X on holiday and would love it if Mary could join us. We plan to stay in half board hotel and would be happy to cover Mary, if you would feel happy to cover the cost of the flight, which looks like being in the region of £200. It would be great if she can join us but we totally understand if it doesn't work for you'
OR
'We are planning a holiday for next year to X. DD wonders if Mary would like to join us. We would be really happy to take her if you were happy to cover her main costs, which are lookimg like flight £X, hotel £X and activity package £X. We realise it's a lot of money and also that it might not fit with what you're doing, but thought we would ask.'
Personally I wouldn't feel happy offering no3. Really I would only ever offer a holiday where an extra child could be accommodated and transported with little extra cost, but I would be perfectly happy to feed and entertain them during the week....but people differ.