Honestly, the first two seem pretty standard to me - looking at it in context of him having two promotions, going from being a dev (I assume) to being a VP of Tech. When you become a manager, your attitude changes, whether you're actually putting in more hours at the office or not, you're exponentially more stressed, and almost never stop thinking about work. Not hard to imagine this would translate to the things you describe - You don't see him working any more, but he feels A LOT busier; He seems more short, saying he doesn't have time to talk about it, so he leaves notes. He gets frustrated with having to guide our daughter through her homework because he's having to handhold people at work all day, and sadly, he doesn't have much left when he gets home.
I know when I became a manager, before I had time to really adjust to it (and some effects persist even after) my demeanor changed a decent bit, I became more impatient, shorter attention span, got frustrated more easily, etc - if you talk to me, I want you to get to the damned point, I don't have time or mental capacity for useless detail. I don't want to be bothered about small things - I make decisions and solve EVERYONE's problems all day at work... I don't want to have to deal with little crap that my partner should have been able to handle on her own when I get home. The list goes on... so yeah, it sucks, he needs to find way to deal and handle it better, but the first two aren't surprising at all.
The third... definitely less OK. I mean, you really gave absolutely no context - what lead to the blow-up, what did he actually say? etc. Without that I can't agree or disagree with people here suggesting he's sexist or whatever else, but it surely seems dickish either way. I can say though, this could tie in with the first two, another side effect of new and unwanted responsibility, feeling like you're constantly making important decisions for everyone - I HATED having decisions or actions questioned after I made them, I also went through a period where, in order to feel qualified to do that (make decisions for everyone) I had to develop an absolute confidence in my decisions, so someone else telling me what to do, or that I'm doing something wrong, was a big hit to that... this one I grew out of with time.
The car. Yeah, no excuse, dude was wrong and he knows it. I can somewhat relate (don't agree with his spin on it) to how he feels about Starbucks... my ex and I actually had the same financial agreement, both have to agree on anything over $100... so she went to Starbucks every day, and shopped here and there spending $30-$40 regularly... it basically just made it so that when I wanted something, I just didn't get it, because despite making a lot of money, I felt like there was never any for me. All of that said... a car? NO.
Overall, I think it's probably easy to think he's making more money and just got an inflated ego and became a rich prick... It's possible, I'm not so sure though, most of the behaviors you describe seem pretty related from someone else who had a lot of professional responsibility quickly thrust on them. I would suggest taking that approach, talk with him with that in mind, that while he may not be in the office longer hours, his mind is almost certainly much more taken by the office. Let him know that you understand he's stressed and doesn't feel like he can handle as much at home as he used to, but his additional stress doesn't reduce yours, so he can't dump things on you or treat you poorly, he needs to find other ways to reduce his load, like a housekeeper, awesome dishwasher, whatever.
As far as the finances... maybe instead of the "over-under X purchase" agreement, the two of you could have specific allowances per month or week? It gives you both flexibility to buy what you want without question, without allowing small purchases to run away, or larger than agreed purchases to be argued. My wife and i actually have a joint account and separate accounts, about 75% of each paycheck goes into the joint, and we each put the other 25% into our personal accounts. Mine is more, because i make more, but it's proportionate. At the end of the day those personal accounts would still be "joint" money in an emergency, but for the day to day, she doesn't ask about mine, I don't ask about hers.