If dining funds are going to be tight take a good look at mousesavers.com for some good tips. Where are you staying? Are you driving or flying? Either way we always take one suitcase full of snacks and treats. I go to our bakery outlet store and buy the mini-muffins, granola bars, protein bars...things we can grab and go for breakfast. Then there are a lot of great counter service locations that offer 'better' dining options. Seasons is my favorite and I always get a kids meal when we eat at Seasons so I can split a treat with my husband.
If you do splurge for a character meal you could opt for breakfast or a late lunch for the cheaper prices. Another option you might consider at sitdown meals would be to order an appetizer for your meal instead of ordering off of the kids menu. When our girls were younger and couldn't eat a full meal they would sometimes order an appetizer as their meal because they didn't want hamburgers, chicken nuggest or pizza. My girls have never been 'kids meal' kids..but as a mom I made them eat whatever I fixed for the family...so nuggets and hotdogs were never an option at home.
I know it stinks that 10 is an adult...but try to stay positive and don't let it ruin your vacation. Plan accordingly and enjoy your time with your daughter. Good luck and have fun!