Ok, just to clarify:
They tell you after the fact, that you signed the "wrong" form.
Did THEY sign this form too?
Did you read the form, and, if so did it seem reasonable to you? (That is, you signed a form about adoption/purchase of an animal, the appropriate form to sign under the circumstances. You weren't signing a building lease.)
Was there any verbal agreement you gave to them about not breeding?
Here is my opinion from what I understand at this point:
They are being manipulative. Bait and switch - intentional, or not, on their part...doesn't matter.
Sounds like THEY signed the wrong contract. Though cookies for them.
You are fully within your rights to be firm about what YOU agreed to - there is NOTHING else to honor!