I do not see anything that unusual about people paying to attend a childs birthday party.
For example, for Little Legalseas Leventh Birthday party we chartered the Island Princess for a week-long cruise around the Polynesian Islands.
Mind, it costs us almost $3.5 million dollars to charter this cruise ship, so we felt fully justified in asking each guest to pay $8,459.98 for an inside cabin ($10,567.98 for an outside with obstructive view; $15,672.12 for a Veranda cabin, and $23,999.51 for a suite; children under age 4 months went for 8/9ths of the regular fare). Most meals (save for lunch and dinner) were free (although there was a $14.99 handling charge for breakfast). Little Legalseas Eleventh Birthday cake was absolutely free for the children to look at behind the plate glass window (only $1.99 to enter the Birthday Cake room, and $5.99 for a slice of cake (non-corner piece). To depart the ship at each port was also free (and only $30.00 to re-enter the ship). For the adults I felt the mandatory 5-drink minimum per day ($45.99) was very reasonable ($11.99 for each drink thereafter; more if you wished alcohol in the drink).
Anyway, you never heard such bellyaching! I still feel that requiring each birthday guest to hand over their credit card for the duration of the cruise was not unreasonable. Anyway, the moral of my lesson is: get the cash up front.