I think you gave away too much at the beginning. I understand you want to be cooperative, but she is not this child's parent and she has no rights (it's even in the legal agreement). The child is 3, and shuttling her back and forth from her mother to a non-relative makes no sense. And I say that as a stepmother who very much loved two stepdaughters - who never came to me if my husband traveled on business.
If you want the child to have a relationship with this woman, and if you want a break (which you deserve), that's one thing. But I wouldn't write up a formal agreement about visitation that locks you into something that may not fit your schedule.
You don't have to answer any of her messages. You don't have to answer any of his messages that deal with things other than your daughter's health and wellbeing (vs. the needs and wishes of her stepmother). If he can FaceTime his daughter, for example, I'd agree to that. Anything related to extensive and formalized visitation, I'd just say "I'm following the court order." And nothing else.
If he and she want to go to court (which he can't do while employed), that's on them. I wouldn't pay a dime for it out of your pocket though. If the stepmother calms down, you can consider what works for you and your daughter - an occasional day at the park or the Children's Museum, maybe an overnight. But I think it's going to be hard on your daughter to live in 2 places when her father isn't there.
Again, I support loving and caring stepparents, but if this isn't working for you and it has nothing to do with being jealous of the stepmom, then just be the mom and not the one who is trying to keep everyone happy against your own wishes.
You don't have to go to this fight just because they invited you into it. "I see I made a mistake in suggesting every other weekend, because it's not enough for you. I'm pulling back to the legal agreement and following that. Arguing about it is not good for any of us and it's detrimental to little Susie to have this tension going on. I'm not going to discuss this further." And don't.