I would suggest you stop worrying, or even thinking briefly, about whether she's going to get a job, or how she will get her act together. You gave her a hand up, when you let her move in for a very low monthly rate, but she didn't use that time to straighten things out.
So stop thinking about anything except the legal ramifications of having someone's stuff at your house, and a non-family member having access to your house.
Was there anything in writing? Or was it all just a handshake and a verbal agreement? And where are the children living/sleeping/eating? If they're at your house, and the parents are not, consider calling Child Protective Services.
Give her at least 30 days notice and then sell the car and the stuff, or take it to the landfill or a donation center (depending on whether it's usable or not). If it's not junky stuff, often a place like ARC or Salvation Army or Goodwill will come pick up a load with a truck. If it's trash, you may have to call a place like 1-800-GOT JUNK to come get it. Or you can put it all on the curb and advertise it on Craigslist under the "free" section. Just tell people to come get it and they will. You don't need to interact with them, just make sure what is to be given away is clearly marked and that none of your personal things are out there. Take the ad or post down when everything is gone.
The answer to your question about "how long to sit and wonder" is zero hours and zero minutes. Take action now. If there was a lease, consult an attorney about what to do. If there was a just a verbal agreement, give her a warning (in writing, and save copies) and then get rid of stuff, get the children into protective care, and change your locks. Don't let sympathy rule here. What you did was nice, but sadly, your generosity was ground into the dirt.