Start a log. Dates, times, and very objective reports of behaviors: '9/11/10 at 2pm: Ms. X arrived at house in tears.' Include specific quotes from her, keep a record of text messages, emails, etc. If she's showing up at your house or calling you, there's nothing to stop you from making a recording- you can do whatever you want in your own house. On your own part, try your very very best to not feed into any of her behaviors.
It's truly sad when a person has a mental illness, but when a child is an innocent bystander that is even harder. It really is up to your husband more than you to stand up here- you are the stepmother. As far as the girl calling you mommy- I would recommend against that at this point, but suggest another special name that would validate your unique relationship. It could be anything, from Sugar Pie to Wolverine for heaven's sake, the point is the girl wants to feel close to you and celebrate your relationship. As the big girl, help her do that in a way that doesn't threaten her mother and cause her more issues.