Hi, I'd like to help you with your question.
It sounds like your daughter is either not willing to help herself because of laziness, fear or she is depressed. Either way, you are going to need to set some deadlines to get her to move out of your home and on her own.
So far, it sounds like she has had little reason to be motivated to help herself. She may be scared to do so. It seems that since her husband left, she has lived with others. She may fear living alone. But she needs to face this fear so she can be independent again.
Talk with her about setting a deadline for her to move out, maybe six months to nine months from now (or whatever time frame you are comfortable with. Just be sure it is reasonable). Then set up a schedule with her with deadlines for finding a job. Start with a certain amount of resumes she is to send out each week in her search. While she is at home with you, have her complete chores. Let her know that she will owe money towards the costs of the home by a certain date, say two weeks from now. But do not change the move out date. If you start giving in and moving the date, she will stay indefinitely.
Remind her often about her move out date. Discuss her progress with finding a job. Keep the topic out in the open so she knows you are thinking about it and that it is a real deadline.
If she needs help, guide her to those who can help her. She needs to learn to rely less on you and start making connections in the community. A therapist would be a good person for her to work with to help her deal with her feelings about living on her own. Also, a career counselor could help her as well. She can contact her local community mental health center for help. They have many resources to help her get back on her feet.
If you are willing, you can offer to keep her kids with you until she settles in her new home. She may feel overwhelmed at first and need time to sort things out. Make it a set time frame, say two weeks, then send the kids with her.
She could also live nearby you, if that works for you. She could still have the security of having you close, but not be living with you.
I hope this has helped you,Kate