The rules??? For you these are the rules. For others? Not always the case.
OP- Whenever we have asked kids to join our family on vacation we have paid the freight. TO be fair, we never went where airfare was involved.
I will say that no matter how well intentioned your invitation was, it is not a surprise that the parents have not responded yet. You asked them to allocate a large sum that did not include spending money, and I do not know many families who would not need time to discuss this.
I will also say that it is better they are thinking about it rather than agreeing and then dropping it in your lap.
I am going through something similar yet pretty different now. Last year we went on a pretty expensive trip, and offered to bring the two little girls on my street with us. We would pay all of their expenses. Now Mom wanted to kick in her share for her trip, and we agreed to that. By the end of the Summer, she had not saved one penny, so what she said she would pay was reduced to "how about paying for the family hoppers once we get to WDW. DH paid for two rooms at the Grand, club level,
DDP on one room and DxDDP on the other so we would all have plenty of credits to take the kids to every Castle, character meal, as well as experiences for all the adults. He also bought all the girls spa treatments at Senses, paid airfare. My DD and I bought clothes for the kids. Mom managed to sav $300 fr spending.
Okay, everyone gets the ride with us one time, and we knew she meant well but did not really. Understand what Disney was.
FF to this year. Mom discusses a WDW with the kids, and asks us to go. I book a BB at POR so we have at least one room only discount. At Christmas we all discuss it, and Mom really wants CL again, but we need to change resorts. Okay, we will move to BC, Mom can enjoy Epcot while my DDIL and I take the kids to the parks, but Mom...CL is wicked expensive. Not this trip. Mom tells the kids! YAY! They are ecstatic, and have been working on goals Mom put into place as a condition to the vacation. Keep in mind DH and I always pay for the kids. All the kids expenses. HEre we are..... It is the end of April. Mom says she cannot afford Her share of the trip. How much can you afford? None of it. She dumps it in Dad's lap. Let Nana take the kids, they know about the trip. I cannot. So.... I am not committed to two rooms at the BC< my DS and DDIL are locked in, as am I with my DDIL....who is on her "free ride" with us. It is all riding on hoping Mom was able to guilt Dad into allowing his to girls to travel 1500 miles from home without a parent. It's a mess.
I am so upset. This is not about money any more. I have two little girls who I love as much as my own grand daughter (who along with my DD is planning to join us for a long weekend on this now trip from hell) who will not understand why they are not going with me if Dad says no. DH is fuming, and I know that even offering to pay Mom's way again is not the answer, she just does not want to go. And it was HER idea.
All of this long story is just to warn people that you never know who things wil turn out when money is involved, and when people want to back out of a commitment. It happens all the time.