then he will be the perfect dad she believes I prevented him from being will he?
This is what I think you should address. Don’t let her go through life believing that her mother is the reason her father doesn’t see her as often as she would like. You’re her only “real” parent, it’s not going to do her any favours to believe that you’re deliberately sabotaging her life.
Yes, it will break her heart to know her dad cba to be a proper parent to her, and obviously you have to deal with it very sensitively and age-appropriately, but it will break her heart more in the long run to develop a pattern of getting attached to people who don’t care about her, and to grow up thinking that the one parent she can count on is actively trying to spoil her happiness. You are there for her and she needs to know she can trust you.
I’ve been through IVF too and I know exactly what you are saying about the timings in this situation; sounds like it’s a lovely cast iron excuse for him to do what he always does anyway, but with the perfect get out of jail free card this time. He sounds awful.
Can you try to find some way of telling her something closer to the truth? And explicitly and emphatically that it’s nothing to do with her and everything to do with him. Try to manage her expectations of him. Your DD may actually thrive better without him keeping her hanging on a string all the time. It really cannot be good for her self worth.
Speaking from experience of growing up with a father who cba to be properly engaged in my life, though different circumstances. You internalise it as a child and think it’s your fault. Make sure she knows 100% it isn’t.
Sorry he’s such a shit to you both and especially to her. 