I am not a new father, but I have 5 kids and raised a sixth, whom we failed to adopt, from new born to potty training, so I have some idea what I’m talkng about.
First, yes everything your talking about is normal, and at the same time, it is normal not to go through this. Our oldest are twins. For one, I was the center of the universe, except for feeding. (The only one of our kids who would take a bottle was the boy we tried to adopt, who obviously only ever had a bottle. Maybe those new ones will work, but you’d better find out.) At a slightly older age, when we did the classic Olan Mills trips, she was only happy while waiting when hunkered down with me. Mom was ok, but I was security. Her twin sister had no more use for me than I do for a tampon. Yeah, I would change her diapers and sing to her and everything, but if she was upset only mom or Father Time made a difference. Sometimes she would look at me as if wondering, “What the hell is he here for?”
Second, try lots of positions. Occassionally, try a position she didn’t accept before. They change every day. For a little while, the belly head down on your extended legs position mentioned above worked for some of them. It never worked at all for others. All part of the fun.
Third, putting her in the crib and walking out of the room is much better than risking snapping. I had an aunt once tell me that if you need to, put 'em in the crib and walk once around the house. I found that when all else failed putting one in a crib and listening to a favorite tune or a bit of TV helped. A few minutes crying alone in a crib won’t hurt her. Anything is better than getting so frustrated you might hurt her.
You are going to fight with your wife more. You are (both) tired. You are (both) frustrated. You have more things to argue about. Even though couples with children are supposedly happier in their later years than couples without, children are very hard on a marriage. They say couples fight over bed, money, and kids, and babies impact all three.
On the plus side, you will soon be building many happy family memories that might keep you together through rough times in your marriage. I’ve been married over 20 years, and yes there have been times I felt like walking. But, the thought of not seeing my kids every day always pulled me through. And let’s face it. Make up sex is about the best. When they can sit they are more fun. When they can crawl they are more fun yet. When they toddle they are even more fun. (I never minded the so called terrible twos. Yeah, they say “no” a lot. It’s not like I hadn’t heard it a million times before. :D) So far, every age is the best age. Once they can sit.