Try calling one of these...
http://julieslist.homestead.com/EmergencyHousing.html
It is a list of emergency shelters in the detroit area.
Look for one that offers transitional housing and is for women with babys.
Not all shelters are like the ones everyone thinks of when someone mentions shelters.
My mom lived in one in PA for 2 years that was apartments that were specifically for HOMELESS women WITH CHILDREN. They did charge rent but it was based on your income and they assisted you with getting job training and financial counciling so that once you were on your feet you knew how to handle yourself and keep yourself there.
You sound like you have a house full already. Please do not cause problems in YOUR marriage so that you may help someone who got herself kicked out of someone elses home.
You need to remember that you are hearing one side of a story and making judgements on that... Have you talked to the BF mom? to find out WHY she kicked her out? If you do really want to ask her to move in, make a phone call and ask the BF's mom some questions. My sister is also a sheltering kind of person and has had a lot of things stolen from her house and lies told to the neighbors from people who looked and acted like family for YEARS then as soon as they moved in and were around 24 hours a day their true selves came out. Thankfully she also realises eventually when she is being used and kicks the ones who deserve it out...
Call a bunch of the shelters and ask them what the living arrangement is. What the cost is. If they have openings and explain to them the situation. She will probibly be deemed as an emergency situation and they will make room. If you have time get the addresses and drive by.
Good luck and hope she finds something...