Only pay what you have to in order to live, keep a roof over your heads. Cut all non-essential spending; don’t pay any credit card or medical bills you have, they are secondary to keeping your home. Do keep your utility bills up to date, and work on getting your mortgage and equity loan up to date.
Do you have any family that can help with either the kids (so you can get a 2nd job for a bit) or with essentials?
If you get calls from creditors, don’t talk with them (unless it is the mortgage or home equity company); they can’t get blood from a stone and you don’t need the anxiety the calls will create. If you talk with them, don’t make promises, just tell them you have no money. If they sue you, they can’t take your home; they can only get about 10% of your gross via garnishment and that’s after several months time (It takes about that long to get the judgment and file the income execution). Hopefully by then you would have turned some of this around.
You could consider selling your home if you can get anything extra out of it over the mortgage and equity loan, but then you also have to consider what it would cost you monthly to replace the living space considering the kids. Not sure if this would work for your situation or not.
Hope this helps some.