You have gotten very good advice. I would suggest that you use time out and not give into your four year old. Parenting is not easy and you need to parent that child even though it is difficult.
Realize that you are but one person and cannot be super mom. Don't be angry at your husband, he's putting in very long hours and is not there when you need the help. If there are things he can help with on weekends, have a chat with him about it. First thing you need to do is get your 4 year old under control, she should not act any differently towards you just because your husband has to work. You're the boss and your 4 year old needs to know this. Since you and your husband have his son most of the time, is it possible to have him put in the same school as your daughter? This is not a good situation for these kids, because one is always going to be waiting. Is it possible to have the mother pick up the boy and meet you with him where and when it's convenient? Your husband and his ex have to come up with a better plan because this is not fair to you or the kids. They aren't doing all the rushing around to get both kids so they think nothing of it, and it needs to be addressed. If you have him most of the time I see no reason for him not to go to the same school as your child. Allow the children to help out and each other, there are lots of small things they can do to help you and themselves. Crack down on your 4 year old and get her under control. It's not your job to keep everyone happy, and it appears that the worst thing is getting both kids on time and I feel this can and should be worked out. With 4 kids you are going to be very busy it goes with the territory and that's why you need to delagate little chores to your children. I think it would help too if you could get away for a few hours on the weekend for some "me" time. It sounds like you have a wonderful husband who is a good provider and this often requires long hours at work. Just think of what you would do without him and the income...this will help put it all in perspective. Sit down and make a plan on how the children can help and prioritize things in your life. It's going to take some time and effort to get your 4 year old under control, but it will be well worth it. I raised 3 with a husband that worked 12 hours a day 6-7 days a week, so I know what you're dealing with. Teach your children to be as self sufficient as possible for each of their ages. Realize what actually has to be done and what can wait. I wish you all the best and hope this helps.