Micaela,
Before you talk about qualifying, let's talk about what you can afford. Sometimes you qualify for more than what you can handle. I think you should assume some type of car payment when you work out what you would be ok spending on a mortgage. I'm not saying get a car before the house, but it sounds like you'll need one sooner than later so plan ahead. I know this sounds like a pain, but it really is the most responsible way to start. Once you come up with a housing number (say $1000), then you would subtract taxes and insurance from the payment (maybe $100 for taxes, $40 for insurance) and you have $860 monthly (includes PMI, maybe $50, on FHA or MyComm which you could get for $0 down likely). So you have $810 per month you are willing to spend on P/I, which at 6.75% (high cushion) you could 'afford' a $125,000 home. Possible you could qualify at that, especially without the car, but you might look at what you have left over every month and realize you need more to live on. Accept that you will make some sacrifices for home ownership but with children you definitely need some discretionary income. Generally the borrowers I have that find a number they can afford, 9 out of 10 times they qualify, gee imagine that. The other 1 time they miscalculated... 
The 3 main areas of qualifying are income (stability), credit and strength of home value. You have the stable income and credit it appears, it's a matter of how much you can afford (and qualify).
2nd, ask yourself what your future plans are. You seem to be stuck in something with an unclear future at the moment. I would caution that it is NOT the best time to buy. Who knows what will happen a year from now (get back together but he refuses to live in your house, etc.). You don't want to be upside down on a home you financed for 100%. My suggestion is plan for a house when you clear up your marriage situation, especially for the legal ramifications. You can also decide whether what you can 'afford' is going to be good enough for your family.
Hi Micaela,
I'd agree with phxdevil. Since you're separated, I'm guessing that means a divorce is possible in the next year or so. That would probably be more complicated if you buy a home before then. Also, if your husband's income is 3x yours and the kids are with you most of the time, then I think it would be reasonable to expect some child support. You might want to wait until you get all of those things stabilized.
By the way, I lived in the house with my ex-wife for 6 months after it was over before finally moving out and now realize that it really is better to finalize things (for the kids, and both parents) sooner rather than later if that is going to be the eventual outcome. Our children were young (2 and 4) when we divorced, and I think it was much easier on them because they were young. I know those decisions are never easy, though.
I'm planning to be a house in the November to December timeframe, and really don't see any advantage to buying before that time. I don't think anyone is projecting for home values to increase much before then and they may even drop in a lot of areas, and in general homes sell for less in that timeframe than in Spring/Summer timeframe.
Good luck!!
I'd agree with phxdevil. Since you're separated, I'm guessing that means a divorce is possible in the next year or so. That would probably be more complicated if you buy a home before then. Also, if your husband's income is 3x yours and the kids are with you most of the time, then I think it would be reasonable to expect some child support. You might want to wait until you get all of those things stabilized.
By the way, I lived in the house with my ex-wife for 6 months after it was over before finally moving out and now realize that it really is better to finalize things (for the kids, and both parents) sooner rather than later if that is going to be the eventual outcome. Our children were young (2 and 4) when we divorced, and I think it was much easier on them because they were young. I know those decisions are never easy, though.
I'm planning to be a house in the November to December timeframe, and really don't see any advantage to buying before that time. I don't think anyone is projecting for home values to increase much before then and they may even drop in a lot of areas, and in general homes sell for less in that timeframe than in Spring/Summer timeframe.
Good luck!!
