First and foremost othstr; many many many congratulations on your beautiful son.
Secondly, do you have any idea what an inspirational and awesome person you are?
Your Hs behaviour would have made most people drop to their knees but not only are you caring for a little one, planning your return to work but GAL like a demon as well.
I would just shrug my shoulders about the phone thing. It's what teenagers do to cover up their social awkwardness. It is a bit different in that he isn't coming over to eat cake; he's coming to see his son. Whatever we all think about him, your son deserves to have his Dad in his life where possible. Setting a boundary may mean that he doesn't come. So just shrug your shoulders and think he's a childish jerk and ignore him. I know you can do that because you are so strong.
In respect of his interactions with the baby: On another site that I frequent one of the common sayings is 'trust that he [censored]'
I doubt even the most eloquent of advocates could persuade the world that your H has acted like a good guy. He [censored]. That doesn't just apply to his R with you at the moment, but in everything that he does.
You don't need him. If he chooses to want back in your life and you choose to let him, then that is because it is what you want, not what you need.
You're doing great. You're doing great despite a mightily shi*** situation. Your son is blessed to have such a strong mother.