It sounds like the communication between you has completely broken down, but if you love him then there are things you can do. It's not irreparable.
Tell him what you need without blaming him. "I love spending time with you and have so much fun when you are present with me and the baby. Can we try to do more of that in the evenings, without the phones?"
Give him small compliments throughout the day to lower the current tension and let him know that you love him.
Most importantly, give up on being right. Arguing does not help anything. You are two people with entirely different perspectives, standards and expectations trying to agree on everything - you just won't! There's no need to hash out every little thing because you're not going to see things the same way, and that's fine.
If he disagrees with you then ask questions to understand why, rather than dismissing his views and just going back and forth until one of you relents.
Instead of trying to place blame or convince him to do what you want, acknowledge his feelings and preface your statements with "I feel/I want" rather than "you've done this/you are wrong/we need to do this" which will put him on the defensive, and then ask him what he thinks a good idea would be.
For example, "I understand that you feel like I nag you. I just feel frustrated sometimes when I have to remind you of things so I feel like you haven't listened to me. What do you think we could do about that moving forward?"
Most importantly, let go of the little things. I don't know what your everyday arguments are about, but if it's not important then just let it go. That's key to a happy relationship, I think.