It is your responsibility to discipline your child. Being a pushover is a kind of cop-out to me. It sounds like you are looking for a father for both of you. Why are you asking him to do something that you should be doing?
First of all if you need assistance disciplining your daughter. Get Professional help.
You are responsible for her well being and safety. If you are trying to build that dream situation, don't use your daughter to do it.
Don't create a situation that you will be sorry for. If you put him in control he will be in control of both of you at this point. Ask for his opinion in private, but you delegate and follow through.
One year! He is still a stranger. so to speak. It sounds as though he has not asked to be included as far as speaking to her concerning discipline, so why are you trying to push it on him?
Spoiling a child other than your own might create other problems for you and her. Get some Professional assistance to help you be more assertive in disciplining your daughter. You really don't get a second chance when raising a child. He is not her father, so don't try to make her fit into that mold. Yes she is suppose to treat him with respect.
Mother, is not just a word, but a state of mind. Good luck to you.