My husband is a very "hands on" dad. Problem is he was raised by "hands off" parents. In addition, he's an only child and only grandchild. He never had experience with a child before our daughter. When she was 6 mo old, I went back to school. I went during the day and he worked in the evenings. At first, he to was very scared but he eventually got it. It just takes more time with daddys than it does mommys.
As you know, the female and male brains are different in many ways. Reassure him over and over again that he is doing a good job. When you are at home with him, lay it on thick. This will build his confidence and therefore he won't be so stressed. The baby is probably responding to his stress and that is the reason she is crying. This is on top of a change in routine. Try to picture it from her perspective. She's leaving a comfortable, normal routine surrounded by people that she loves and takes care of her to someone who is nervous and scared. She doesn't know if she can trust him and that scares her.
The best advice I can give is just reassure him while you are at home. Also, do activities where all three of you are involved. This could be something as simple as rolling a ball on the floor to each other. In addition, plan an activity with just daddy and baby with you sitting on the sidelines. She will be comfortable because you are there, but she's getting bonding time with daddy. This will also ease his stress as well. Let her see that you are comfortable around daddy and she will too.
Don't forget about your stress level. She will respond to that as well. If you leave her with daddy and you are stressed, she will pick up on that.
Just be patient. Things will work out. She will eventually get used to Dad. As far as him calling, tell him not to call unless it is a true emergency, aka going to the hospital. Also, give him a list of numbers to call if he needs help. One suggestion is calling either of your mothers. Tell the mothers not to go over there and take over, but to calmly assess the situation and make a suggestion. Stay on the line until it is resolved. This will also build his confidence because he did it, not someone else.
Sorry this is so long, but I've been there. Don't worry. He obviously cares for her. Things will work out.