It’s always good to be clear….as people have different expectations and that can cause misunderstandings and awkwardness or stress, so good to communicate now about it.
We’ve often taken other children on holiday with us and always covered the cost. We invited them and so they were our guest. They always came with some spending money and some had clearly been told to offer to buy a meal out or ice creams. We’d let them buy ice creams, but not a full meal.
Sometimes our children also got taken away by other families and similar happened.
If it was the first time a particular child was coming with us, we’d always text something similar to the suggestions mentioned here….that we were thrilled X was joining us and that we would all enjoy their company. We would mention that they might want to just bring a little bit of spending money. The fact this was said, made clear we didn’t need anything for the cost of the holiday. Usually it was self catering, so accommodation didn’t usually cost more, but there were costs for eating out, activities etc but we were happy to pay them.
Amongst the families of our kids’ friends, when they were smaller, they’d often get taken out for the day with another family or we’d take a kid along with us. The host always paid and no-one really seemed to keep count. It was just how it worked in our group. I realise not everyone does that.
It’s tricky to invite someone to come away with you and then to want them to pay their way, if you’re talking about a child. The only way I think that could be okay is if when the original invitation is issued, the amount of money it would cost them is mentioned. Otherwise they can’t answer in full receipt of the relevant information.
There are often threads on MN about this kind of thing when after agreeing to take a child, the OP wants to ask for cash, or after someone has accepted an invitation without mention of money, the host has asked for cash. It really has to be mentioned at time of invitation if money will be required. And personally, I’m if the view that if you aren’t going to cover all or the bulk of their costs, don’t invite another child.