As a stepmother, I can honestly say that I do not expect my stepkids mom to send money with them when we go on trips (or anywhere else). Sometimes she does and that is nice but she usually does not. If it is a bigger trip (the beach, WDW, etc), I make sure that the kids have saved up money they get here (from my family and DHs family for birthdays/Christmas, etc) or I give them extra opportunities in the weeks leading up to the trip to earn extra money from DH or I. Once they get where we are going, the money is theirs to spend how they want. I have more important things to worry about than making sure 'our money' is only spent on people here and 'her money' is only spent on people there. I do however make sure the kids realize that when the money is gone, it is gone. And, even though the children I gave birth to are significantly younger than my stepchildren, I also try to make sure that when we are all somewhere together, they all have the same amount of spending money. I try to not be an ATM for my DDs while the stepkids are walking around counting their pennies. And to answer your original question, would I send money with my kids if they went with their dad? It depends on the kid. My stepdaughter for example would spend all of hers within the first day or two on candy and still not be able to get something neat, regardless of how much money she had.
This was her third trip and she was still a Disney Princess. She was clearly the center of all our Universe. A young couple boarded with an infant and a little girl. You know the ones..........new family but forced to bring the child from the first marriage along. She was about three and terrified. The "family sat together and sent the little girl down to sit with me. A man behind the man offered to move and was told no. This little girl held her little toy and told me it was how she did not cry. I spent the ride talking about the characters on the video and showing her sights from the bus window. My heart still breaks for this little girl who was included on the vacation but clearly not wanted. 