My husband works full-time and I was a SAHM until my son started Infant school. I did the bulk of the chores at home as well as looking after our son. However, my husband didn't sit on his arse and do zero at home in the evenings/weekends. He was, and still is a fully engaged parent and helps me where he can.
Your situation is different. You have 3 children, you are home-schooling 2 of them and your husband doesn't help at all.
Your husband should be a fully engaged Dad once home from work. Disappearing off to his home office after he's eaten, means he's spending no time with his children or you. He may be in a job he dislikes, and has stayed because it pays well (some people have little choice but do this) but that isn't an excuse to disengage from family life. Nor is using the excuse he works full-time, there are plenty of parents who work full-time, who are fully engaged with their children.
The current set up isn't working for you as a family. Tell your husband that he needs to be a present Dad to his children in the evenings and at weekends. His children must barely see him, no wonder they won't settle for him! He needs to start helping you with bedtime, regardless of he wants too or not. He chose to have 3 children with you, they aren't your sole responsibility!
You need to start having an evening to yourself, where you go out. He then will be responsible for getting the younger children settled, even if you've helped with bath time. Join a gym, book club, running club...anything that gets you out the house.
If you have family close by who could baby sit the children, suggest a date night once a month.
If the above doesn't work, you need to back to work and send the children to school. If your husband refuses to help you by parenting his own children, then he's disengaged from family life completely. If he's not interested in a date night with you either or spending any time together, then he's disengaged from you as well as the children. You then need to think about what you want going forward. His attitude isn't going to change. Making sure you're financially independent becomes your priority.