I feel for you sweetie. Most SAHMs have been there to some degree. You are not alone.
Some options...
Is it possible for you to work part-time and your husband cut back his hours a little? I don't blame him for feeling like he is not responsible for helping around the house if he is truly working 7 days a week. But he is still 1/2 of the parenthood and when he is home, he should be just as involved with the kids as you are all day. Maybe though if you were working part-time and he was working a little less, things would balance out. You'd get your out of the house time and he'd not feel so overworked.
As for the kids and keeping your sanity - it is hard, very hard...but doable.
Some suggestions would be to schedule your day with them down to the hour. Always have things worked out so they get used to a schedule and are not bored. The times my children drive me nuts is when they are unoccupied and start teasing eachother. That's when I lose it, but in the end, it's my fault. I should have given them something to do. I would cut out as much television as possible, and the only things they watch should be educational.
At that age, your children should still be taking naps. Use nap-time as ME time. Take a hot bath, get in a quick work-out, or read a book.
Go on walks. It is amazing what a little fresh air can do.
Join MeetUp.com. There are so many groups and events you can go to, with the kids. You can meet some new friends that way, and build your support group.
Try not to gripe. I know it's easy to be ungrateful. But think how it will be if you had to work full-time in addition to your husbands salary. Kids in daycare (sick more often), hectic strained schedules, etc.
Start asking questions...like, "What did you do at work today honey?" "What would you like for dinner?"
Get him involved in conversation.
Sex is hard when none of your needs are being met. If nothing changes with your work schedule, the change you need is all going to be up to you. Join a gym for your health and a break from the kids. The childcare at gyms is very inexpensive and usually high quality. That's two hours of your day you could be losing weight, toning, sitting in the sauna or steam room, swimming, etc. And your children will be getting some socializing in too - happier kids for you! Most gyms are waiving fees right now for New Years Resolutions promotions, so it's the best time to get in.
Onto the husband...he won't change unless he sees that you are happy with his efforts. Which means that he is getting what he needs from you - and if that is sex (of course it is!) then that is one of the answers. I know it sounds crazy! But lead by example.
Simple things you can do...make his coffee for him and have it ready when he gets out of the shower. If he likes to read the paper or jump on the computer when he gets home, have a snack ready for him at that location. Write him silly love notes on the bathroom mirror in lipstick or on a post-it. So he will see them in the morning when he gets up. Help the kids make handmade cards for him to read when he gets home like, "Thank you for working so hard for us! We love you!" You may see that he starts doing more little things for you that make you feel good...then the whole sex dillemma ususally flies out the window.
Read the books: "The 5 Love Languages", and "The Proper Care and Feeding of Husbands." You'll gain so much from them. The second is catered exactly to your situation - and even though the title sounds condescending, you'll get more out of it than him.
Find a babysitter and schedule two date nights a month. Choose an activity that you two can accomplish together, frequently - like hiking or attending a frequent event that you both enjoy.
Are you goals the same and are you both focused on them? Finances, religion, future family planning, vacations, retirement, kids education? If not, your life will always feel like chaos. These can sometimes be tough discussions, but they must be had.
If all else fails, seek counseling. Your life is completely unbalanced. As is his. You may need a neutral party to help you sort it out.
Best of luck to you!