I'm going to throw a few thoughts out there as a person who has been married one year and is fairly certain that my marriage is going to go through a serious rough patch in a few years when we have kids.
Your communication styles aren't working. And a baby makes everyone tired. Which makes it harder to get good communication going. Serious question-when was the last time you guys when on a family outing or a date for the just parents? Did you reconnect at all? My DH and I work semi-opposite schedules right now, and after basically saying "good morning, good night, and do these three chores please" for 5 or so days, it's easy to argue. But one date fixes the feeling, or hell even just starting a backyard fire and having a drink together. And we have a puppy that needs lots of attention. I can't imagine your crazy animal situation.
In our situation, a budget helps with all of these things. Some of the money you're not accounting for probably goes to random baby-related items, and probably some mom clothing for the crazily changing body of the woman you're married to. Just guessing though. But a budget says we have x to do fun family things this month, and y for hosting people, and q for baby things. We also leave a buffer of $100 for "well we went over this category" instances or times when you just don't have a category to stick an expense in. It really helps frame conversations about, say, heat and a/c for a shed for a cat costing a lot of money. And affecting other things you do.
Another thing that helps is sitting down and figuring out exactly what chores each person is responsible for. You have a long day at work and just want to recharge? Well all day at home with a baby is not exactly kicking your feet up, which you probably know from your Saturdays home with the kid. But deciding that you'll take care of the animals is different from you ending up stuck with them. And you committing do doing the dishes and dusting/vacuuming and then actually doing them goes a long way. Same with her doing the breastfeeding/feeding the kid in general, laundry, errands, planning of events. On a side note, I don't think my husband really understands how much time me doing our mail actually takes.
It seems like you're both a bit resentful of the other person. Being proactive about chores/responsibilities and money can go a long way to solving both. Because now I can be mad at my husband for not taking out the trash because it's actually something he's supposed to do, even when he's tired after work. Which is better than resentfully taking out the trash/feeding the dog/etc. every other day and over months building up anger. Some good conversations, and possibly some counseling, can go a long way in fixing these things.
You've mentioned a lot of things she doesn't want to change when you ask, from rehoming an animal to the thermostat. Before counseling/a big discussion-what do you not change to her preferences?