Who will get the house in my Nevada divorce?

bought the house in Feb 2013. Everything in my name; mortgage, insurance, taxes, utilities, etc. He signed a quit claim deed at the time we closed on the house.
Due to damage he did when drunk and wear and tear/lack of maintenance, I believe, at best, the house is worth what we paid. I am not an appraiser so I couldn't say for sure though. We paid 130k and I owe $120,805.02 at this time so if I understand it correctly, we have an estimated $9195 in equity. He is demanding money.
We have $12k in credit card debt. I tell him if he gets 1/2 assets, he gets 1/2 debt. He says he won't pay the debt or he'll just file bankruptcy. All debt is in my name (he has cards with his name on them). I have agreed to keep all debt and give him two boats, three vehicles and much of the furniture. I get the house, a financed car, a broke down truck and primary custody of kids.
I've been told we don't have enough equity in the house for it to be considered. Is this true? Since he signed a quit claim deed, does he even have any right to the house? If he were to get the house in the divorce, wouldn't he have to get a mortgage in his name?
Since all debt is in my name will the credit card companies just change it into his name? If I do end up having to pay him for half the equity, how long tilI i have to come up with that money? If I have to sell, can I ask for deferred distribution until the kids leave home? I have a lawyer but she hasn't gotten back to me on these questions yet.

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