Why is your son a little King and your daughter only a princess and not a little Queen ???
I suspect you have helped to create the roles you and your husband play.
I suggest that on Saturday, you get up and make everyone breakfast, then pull out the list of chores for the day, while you are all at the table. Ask who is going to do which chore. Don't ask for help with "your chores" -- they aren't yours. You have just been doing ALL of it for too long. The chores are things that help everyone in the house to live well, and they are responsibility of every capable person in the household.
If this doesn't help, and you don't mind a bit of conflict floating around -- you can always sort the laundry and wash only yours and the kids'. He can wash his own. If he doesn't help with the rest of the chores, he can at least do his own.
When my husband and I got married, he already knew I believed in egalitarian roles and I had no respect for men who think they should be king while the women are slaves. He agreed to wash dishes if I would cook. It doesn't work quite that way anymore, but sometimes he cooks and does dishes, and sometimes I do both. We both clean the house, and we both do laundry (although I cringe when he does it, because he doesn't read labels. I work hard not to criticize because at least he is washing and drying it !!)
I would make a point not to try to launch a discussion when he's watching TV or reading a book. Men don't like to be "interrupted" even though it appears to be okay for them to interrupt us. But during a meal, when the family is already gathered, there's not much to do if you don't talk together. I know the kids are there then, but if it's a reasonable discussion, versus an argument, I don't see why that isn't a good time to bring up the fact that you should be sharing the chores and the parenting obligations.
Other things to do? Join a bowling league, so once a week you are out and he is solo parenting. Have him bring the kids back and forth from daycare periodically, too. That's actually what got my husband cooking -- he got home first, and the little ones were hungry and couldn't wait for mom to get home AND cook the meal. So Dad started cooking for them, and he found out he could. Now we share the task. he also absolutely LOVED picking them up at daycare, because he would walk in the door, someone would scream, "DADDY !!!!!!" and two children would launch themselves into his arms. He always said it was the very best part of his day. So, if you have your honey pick up the kids at least once a week, he will be getting a big ego boost -- and he'll get to spend some time with the kids, while you can spend alittle "me time". We all need it, in order to be refreshed to cope with the rest of life.
the other thing with me ? I'm not a stickler for a perfect house. Our house gets cleaned when it gets cleaned, not daily. If my husband is sitting around watching TV, I don't feel like do drudgery work. So I find something else to do. When he's away, I find it is much easier for me to get motivated to clean, than when he's sitting around doing nothing. If the house is less than perfect, your husband may realize with his own eyes that you don't have time to do everything. But when the house looks really nice, how is he supposed to believe you are "overworked"? Obviously you are doing a great job and don't really need his help.
Go to the library and get a few books, so when he's reading, you can be reading . . . etc. When he's coaching, take the kids for walks in the stroller or something. Do something YOU enjoy. Be sure you feel as if you are getting equal treatment, even if some things (like perfection) have to go by the wayside in order for that to happen. what you don't want to do is have resentment fester, because it'll make you feel worse and worse and it'll come out in lots of unhealthy ways.