You don't know me, I'm over in MLC, but I've seen what you're going through in your sitch, and it is a very tough one. I don't know much about why they (WAS, MLCers) do these things, but I do know a bit about the legal process.
I'm writing today because you are, as I'm sure you know, in a very precarious situation all of a sudden. Mediation is one thing, temp order is very different.
I learned from my experience that you generally can't really ask for a temporary order unless one spouse has not been contributing financially throughout the separation. If you are the greater wage-earner, then you should be paying some support all along. If you are the lesser wage-earner, then you should be contributing somehow. Your L should have told you this. Also what you can or can not do now.
Also, the house is a marital asset, she can not just have it. Unless you owe her tons of money and they are trying to settle it out.
Lastly, whatever the courts do decide with a temp order, often it becomes status quo and then when you do go through it officially the courts tend not to want to deviate from this. This has major ramifications for you, if you really want joint custody, which given how you feel about the kids, would seem to be a good thing.
OK, you need to find out NOW what your L has to say. TODAY. You also need to go see some other L's, with other types of strategies, and ask them what you should do / what they can do to help you. Go see them tomorrow, no kidding. Make appointments NOW. You might have to pay them for their time. If you keep it short, you should get away with about 1/2 billing (many will bill by less than hour increments - ask on the phone). When you call them up, tell them you need to see them asap (which is very common in family law). Find out your rights, do not wait to be sitting in court, find out NOW.