Wow lots of little issues here to unpick. Firstly you haven't ruined the family. You have 2 lovely kids. Who is to say that your DS wouldn't have started behaving like this anyway. And pushing boundaries to see what he can get away with isnperfectly normal. So how to deal with it......Firstly you need a structured routine of discipline. By discipline I jist mean he needs to know what is and isn't acceptable and the age appropriate consequence. For me at that age it was 2 minutes on the naughty step, or turning the TV off. However, you also need to try to work to his strengths - so does he play up at bedtime because he is tired? If so what can you do to the routine to make that easier for him? Can you start bedtime earlier? Can you do bath during the day instead of at night? My routine at that age was that after tea around 6pm I would take both kids to the bathroom. Run the bath, toddler in with toys, baby would have a splash at the other end. Take baby out and get her dry and dressed. Put her in bouncy chair or cot while I finish toddler. Then get toddler our, dressed, teeth. Then we would all go into the bedroom. Sit on toddlers bed and do stories while BF baby her last feed. After stories I used to sit a while with the light of finishing the feed. Then when both kids were asleep put baby down and go downstairs. Usually my DH would get in around now and warm up his tea. He didn't always see the kids before bed. It didn't harm their relationship. He was very involved at weekends.
Make sure during the day toddler has lots of activities to tiee him out and give your day a structure. So that might he pre-school a couple of mornings, or a kids music session, or a trip to the library or a play date/coffee with another friend.
I tried to structure the day somewhat so we all knew what happened next, up, breakfast, pepp pig cartoon while mummy showered, morning activity (with a snack break), home, play while I made lunch, lunch, TV, sleep/nap, up, something else - pop to library/shops/grand parents/play in garden/walk to park, home, play, TV, tea, bath, bed. (Breast feeding fell into the quieter times, first thing, snack time, TV times etc - of course some times you have to stop what you are doing to feed).
Your husband crying could be because he is exhausted but could also be a sign of depression. Does he talk to anyone about how he is feeling? There is a free confidential helpline available for all teachers. Please Google it and encourage him to call. This has been the hardest most stressful time for all school staff. He has had to deal with covid and all the difficulties the schools have faced and also adjust to a new baby. If talking doesn't help encourage him to see the doctor.
You have got this. You can do this. It does get easier. If your mood doesn't improve you may also need to see the doctor - because mum's can get depressed too.
Do you have any friends with 2 kids you can talk to? Maybe not with babies the same age, maybe older kids? Solidarity and a understanding can help.
You've always got MN too.