She is clearly uncomfortable with you, so why would you want to continue to rub her nose in it by going to her home etc?
Think about it, she has been with her DH less time than you were with him. She also has a baby. She, for whatever reason, feels threatened by you. It may be ridiculous, it may be justified ( not saying from you, but maybe her DH isn't as good at making her feel like the no.1 woman in his life). She is probaby hormonal/knackered or both. You say he is a wonderful, devoted father. What is he like as a husband? It is not so hard to see why she might feel threatened. What have you ever done to make her feel any differently towards you?
She may be acting like spoiled toddler,but you know what? In a way, by insisting on going to her home etc, so are you.
If it were me, I would be inclined to make a genuine effort to be friendly towards her. Maybe she feels edged out when you are around. Maybe you and her DH make a point of talking about people/places/events that she has no first hand knowledge of. Do you have a new partner? If so, why can't you invite ex and his wife for a meal with you both. maybe seeing you with someone else will show her she has no need to feel threatened.
Otherwise, I would perhaps cool it for a little while. Let her start feeling like a human being again after the birth of her child.
Pleas can I make it clear, i am not in anyway, trying to imply that you have any feelings other than friendship towards your ex. But you know how it is after you have had a baby. You feel so unattractive, so tired, just so very, very, exhausted both physically and mentally, that you really do need your partner to give you confidence, not to insist on seeing the ex, who, in your eyes, is more beautiful, slimmer, no stretch marks etc etc.