I am usually not a fan of using sex as a motivation/bargaining tool...buuuuuuuuuuuut...I have to agree with you on this, D.
I think this is a two part problem. On one hand we have a husband that is just not pulling his weight around the house and with the kids. He's being lazy point blank. On the other hand we have you OP, the SuperWIFE, and SuperMOM that has not said "NO!" to any of the responsibilities placed on you.
I think the issue is that us women take on all this stuff because we feel if we say "NO" then that makes us a bad mom or a bad wife. I think many of us fall into that rut that tells us "a GOOD woman does this," and "a DEDICATED Mom does that," when the truth is that we have to set out own rules for our relationships, and establish our own boundaries.
I know this is easier said then done, because again, I am not married...but, this is a time that you and your husband sit down and talk. and divide up the chores and household duties...and hold him to it.
E.g. If he's in charge of washing the dishes do not lift a finger to do them. Even if the dishes pile up for days, DO NOT DO THEM.
He wants good lovin'? Then get off the couch, make a move, and lend a hand!
He feels neglected sexually, but he has yet to realize how his laziness, and hands off attitude is contributing to his neglect.
I agree, if he had her schedule he'd be to tired for sex.