The charges were just yesterday. Call the credit card company and have the charges stopped.
Then sit down with D17 and have a talk.

Is there a reason she thought she had to go ahead and go behind your back? Was she anticipating you saying No? Which of you are helping guide her through the application process, you or stbx?

It has to be treated as 2 separate issues, as Gypsy said.
You will have to have a discussion with stbx about what costs are going to be covered by support, and which will be split between you.

And D17 needs a talk about college applications, costs and real money, responsibility (does she have a job?), spending as she goes out into her future (she just seems to be set up to create a real mess when she gets out on her own - credit card companies are looking for "new meat," and she will quickly get in over her head).
Point out that her mother said to ASK YOU about the fees - not to steal your card!!
Instead of thinking that stbx wouldn't pay for any of it (which is probably true), think of it as her requesting a conversation with you about it (yes, I know this isn't likely her train of thought, but if you offer stbx something rational, maybe she will take you up on it - say that D17 said she thought you should both talk about pending college steps).
Meanwhile, if there are deadlines looming, maybe agree to give her a set amount of money, then help her decide which colleges to send applications in for.
Point out that most entry-level jobs pay roughly $8/hour - how many hours work is each application worth? Would she be willing to ring out customers at the grocery for that many hours to pay for all that she wants?