Both you and your DH need to sit down with her. "Mom, when you moved in, we said you could do so WITH CONDITIONS. One of those conditions was that you pay us $100 a week. You haven't paid us for X weeks. (insert any other conditions she's failed to meet too) We've thought long and hard about this, and we're not happy with what's happening and we feel this is not working for us anymore. You either need to start paying us what you agreed to, as well as your back rent, or you need to leave by Y date (two months at the most, I'd say, is enough time to find a little place). We'll help you look and move, but if you are not out by Y date, we will move you out ourselves."
Guys! It's not about the money; the money is just one small aspect of why the resentment is so high.
They want her to move out because she is unpleasant to live with--she nags and nags and nags.
(I think part of that hypercritical-ness may be because she is unhappy. Being overly critical or angry a lot is a symptom of depression, actually. This arrangement is probably not good for her either.)
WillyNilly's advice is very good.
And start doing some of the legwork, just a little. Start saying, "Oh, look, here's a nice price on a decent apartment for you, Mom!" As caz suggested, just start having constant conversations that treat her moving out as a foregone conclusion. It'll help make it more real to her.
You might also start getting critical back.--when she nags, etc., immediately say, "You know Mom, that sort of comment is exactly the reason why you need to get your own place, and pronto. It's not good for you to be constantly in this critical mood. And to be honest, it's not good for me. It's making me really annoyed with you, and I *love* you. I hate it. We're in each other's business too much."
Start making "living with you" have some serious downsides. Politely, as I suggested above, but irritations.
(also try making sure she gets out of your house some, to build her own activities in town.)