S.L.
First of all I want to put your mind to ease about the reading. I have always had a hard time reading outloud to children. Like you, it bothers me when they are not listening. But I see others that just keep on reading and pushing ahead and eventually the kids listen. My husband has a lot of patience for this. So in our household, he pushes the reading. BUT, he doesn't have patience for phonics training. So that just happens to me my area. But I've learned that it doesn't have to be done in military fashion. :) A letter here, a letter there, draw it, trace it, notice them in street signs, see videos about phonics, it's all around. Learning to read is a lifestyle. We have 4 daughters and all of them learned to read early but we never made it a hard thing.
Your daughter will learn to read and while listening skills are important, you can't expect every child to be able to sit still and listen at a particular age. It may take her awhile longer to come around.
As for parenting styles.. You will have a long and frustrating marriage if you try too hard to change him. Try to learn to respect the differences you have. There will be things he's good at and things you are. You have a lot of years left to parent this child. It's always nice when 2 parents agree. But if you let your daughter see you argue about things she is doing or not doing, she'll turn it around on you and use it like a wedge between the 2 of you in order to get her way.
Suzi