Invisalign is MUCH more expensive, and because they are removable they require a lot more self discipline to continue. If I could have popped my braces out when they hurt - well, let's just say that I wouldn't have straight teeth now.
That said, do your kids qualify for Medicaid or CHIP? I know Medicaid covers braces, if you can find an ortho in your area that accepts it. I'm not sure about CHIP - but 2000 would make it worth looking into, if they qualify.
I would talk to another orthodontist, or her dentist, about whether or not braces are really a good idea right now. I was told that my 10 y.o. daughter could wear braces now for about a year, for appearance's sake, but would need braces again when she hit 13 or 14 for her permanent teeth. That, to me, seemed like a waste of money.
If your husband has a Medical FSA available at work, that might be helpful too. Most orthodontists offer a pretty substantial (think 25%) cash discount if you pay the whole thing up front and you don't have insurance. A Medical FSA lets you set aside a certain amount for the year, and you submit for reimbursement as you incur costs. The money is taken out of your (his) check pre-tax (which can add anywhere from 5 to 30% to the value) and is available (usually) from the beginning of the year. Then it is deducted, automatically, every month or week or whatever the pay schedule is.