It is difficult to work two jobs. Stressful, and exhausting and in those situations we never act our best. I prepare tax returns and for part of the season, I work 12 hour days, that along with the drive, keep me out of the house 13 hours a day. The kids have gotten on the bus by the time I awake in the a.m., and they were often in bed when I got home. If it weren't for my husband who loves them, handled the family and helped me 'chill out' when I got home, it would have been a disaster. But we managed for 6 weeks. I can't imagine filling those kinds of hours on a regular basis. . . .
That said, I also wonder what kind of household this is, where the animals freely walk on the table during mealtime ? We've had lots of cats over the years, but they learned very early on that tables and counters are not THEIR spaces. The cat should be checked for worms, if it's not getting enough nourishment out of its own food and is stealing from the table.
And then, on to your spouse . . . yeah, I'd go to Mom's and unwind for a while. Don't go angry, however. This is a scary situation for you, and for him. He was out of control, and he knows he behaved badly. You guys were apalled and frightened. If the cat did something wrong and was treated to that kind of response, what happens when the children do something wrong ? You do need to let him know that you care deeply for him, that walking away isn't easy, but that you are also frightened by his bazaar behavior, and is over the top response when he gets angry. If you are going to move out, you are going to have to come to an agreement about money, too -- if you leave, is he still paying the bills ? (yours and his? the babies?) if you stay, you need to make a pact that when the time bomb is ticking inside him, that he pull himself away from family time and go for a walk or something. BEFORE he blows up. Why not round up the cats and corral them behind a closed door so they don't disturb dinner ?
It is up to your husband to set the tone for his relationships with his children. If the relationship is one in which your daughter feels safe and loved, and secure, that is something HE creates. He is the adult between the two of them. But if he is going to frighten and scare her, then he needs to get control of himself and simply walk away when he is angry. No child needs to witness that, and wonder if they are next . . . because sometimes they do bad things, too. . .
I'm wondering about financial help ? What about rental assistance? What about food stamps ? What about a chips card for the baby ? I don't know what kind of jobs your husband has, or the income level, but it's worth checking out what kind of assistance is available, so that he isn't caught in the viscious trap of having to work 24/7 very long. It's just not possible to maintain one's sanity when one is constantly on the go and never allowed "off" time to simply relax. It's not good for him, not good for you, or your family.
Living with the inlaws is also not such a hot place to live. While it's wonderful of them to open their home to you in a time of need, it is incredibly difficult to live in someone else's home for an extended period of time. If adds stress to a stressful situation, and doesn't bring out the best in us. Investigate ALL the options -- where to live, how to do it, what other kinds of support are out there . . .
And what about him working one job, and you working a PT job? You could get in laws and parents to take turns and babysit while you work, and/or you could work different shifts so that one of you is available to run to the doctor's visits and stuff. Leaving all the income production up to your husband puts a heck of a load of stress on his life -- and there are other options out there that might work.
Bottom line? Figure out what is causing the stress. Figure out if there's a way to reduce the stressload. If you want to save your marriage, do what it takes to get the stress lowered. Look for alternatives you haven't yet tried. PA also has daycare subsidies, if you want to put your daughter in daycare and leave just the baby with relatives while you work. It CAN be done, and you CAN get through this. But you have to decide what matters most to you both. Obviously what you are doing to get through right now isn't working. That's not your husband's fault, but it sounds to me as if he's simply the "first victim". Tackle it as a problem to solve, not as a blame game. The problem may not be your husband and his temper, the temper is probably the result of the problem.