This is a very crucial matter to handle and you have to think carefully. This is about your professional career and passion but you can’t sacrifice your dignity for that. You can strictly deny her offer if you don’t agree with her. You can definitely look for other producers. You should have faith in yourself and you will definitely get better opportunities than this.
And unfortunately, yes your show producer can cancel your contract at any moment if you have signed it according to her contract. Unless a contract contains a specific rescission clause that grants the right for a party to cancel the contract within a certain amount of time, a party cannot back out of a contract once they have agreed and signed it. But in your case, I think the contract might have some clause under which your show producer can cancel your contract. Therefore, you should consult a good lawyer and show the contract and take legal advice.