When my husband divorced his first wife, he paid so much child support she was able to remain a SAHM, albeit on a tight budget. Keep in mind, alimony is taxable income. Child support is not. It is in your best interest to receive more CS than alimony.
Typically, CS orders include that the non-custodial parent has to keep the children on the employer-supplied health insurance AND since you don't have any income the order can include that the non-custodial parent has to pay all out-of-pocket health insurance costs. Of course, that means you won't have health insurance (which the ex-h's employer may have a policy against covering you). Since you have no other income, you might qualify for Medicaid. You'll have to check on that.
CS orders also include the requirement that the non-custodial parent pay or contribute toward daycare if you end up having to work. Sometimes the ex-h decides it is just cheaper to pay for you to stay home with the kids. This is especially true if the kids are still young. While CS is supposed to be used only to support the children (ie: you have to support yourself), when the children are very young (not yet school aged) then the courts often agree that it is best for mom to stay home and be supported for a while.
That all said, divorce sucks. It is financially disasterous for everyone involved. Sorry. I don't have any great suggestions. There are people who DO work, even with multiple young children under foot.