You sound Controlling to me. Selfish. Jealous and Insecure.
I can see her quiting if you pressured enough. No money, no where to go with kids, and a controlling husband that would probably fight to keep every extra cent of support money they have coming to them. Alot of woman are trapped in an unhappy marriage for just those reasons.
But I could also see her resenting you and holding it over your head until she had enough strength or money to say, I have had enough.
What do the two of you have in common other than arguing and a lack of trust that would make time spend together more important than time spent apart? When is her contract up?
