asking for your opinion, please (updated)

[Tennessee Dad]

Just looking for opinions; so many of you have already gone through so much.

Background:  remarried Father of 6yo daughter; ex- left me when pregnant with the child, and moved in with her ex-.  She has had a string of men come and go over the years, and lived with at least three of them.  Currently, she has lost her house due to foreclosure/bankruptcy.  She has not worked in two years; her only income is child support and public assistance.  She has moved in with her Mother and step-Father, their two grown sons and one of their wives or girlfriends.  Now BM and her other son (and our daughter when she is there) are also living there, supposedly in the sunroom of their 3br house (according to daughter).  

I currently have temporary custody of daughter, due to three fires at the Mother's house in one week, while she was in the process of moving out.  At our hearing on temp on Monday, Mom was served with petition for change in custody.   Judge wanted to hear no testimony or see any evidence; he did make it perfectly clear he wanted this resolved as soon as possible.  I have records back to 2001 that I have had the daughter more than half the time (roughly 60+%); we have school records backing up this fact.  I have always paid my child support, and provided other needs for our daughter.  I have been remarried almost 5 years, and live with my wife and 15yo daughter from a previous marriage.  

BM has 30 days to respond to my petition, and now I am waiting and wondering what will happen.  She is playing on the fact that she doesn't want her children separated, but my other daughter (who lives with me by her choice) is also a half-sibling.  

Realistically, what are my chances?  Any ideas?  Just ask if you want more information.  

UPDATE:  We have a court date now scheduled for June 4.  This is unless she answers the petition sooner, and we can get it on the docket sooner.  I have been told this should work in my favor, having temp longer, and providing a stable environment.  Any opinions?