I'm sorry that you and your family are dealing with this situation. I know it can be very stressful for everyone.
I don't know how much of this you want to take on but the first step is to sit down and do a very careful budget. You need to include all the income in the household as well as all the expenses, right down to eating out, even if it's just a coffee in the morning. This will help determining if it's realistic to keep the house or not.
Some states have a judicial foreclosure process, meaning the mortgage company needs to present the case in court before they can take the house. Other states are non-judicial, meaning they don't have to go to court, they can just foreclose in the event of non payment.
A typical foreclosure in a non-judicial state can take from 5-6 months counting from the first month you didn't pay. You get plenty of notification by mail to let you know what's going on. Once a foreclosure date has been set you will be notified. They will place adds on local papers advertising the auction date (that's the actual foreclosure date). Most people wait until after the auction to move. If you don't they can start eviction process and that can vary depending on each situation.
As far as your mom getting a break because she's disabled, that only happens if they go to court and present the case. This would happen in a judicial state or in the case of an eviction. But there are never any guarantees she will get a break.
You should definitely try to talk to the mortgage company and see if there is anything they can do. If your name is not on the mortgage, have your mom or dad type a letter saying it's ok for them to talk to you.
Keep in mind that because there are so many people in trouble the whole process can take months. The good thing is that as long as the mortgage company is willing to work something out, the foreclosure can be postponed for quite some time. Again, it all depends on the company and the individual situation.
Check the website for HUD (HUD.gov). Under topic areas they have a section under "Avoiding Foreclosure". You will find a lot of information there.
I would also suggest looking into subsidized housing (section 8) as a possible alternative. Talk to your local housing agency and get more information there. The waiting list for that can be long but you can get more information as far as your options.
One last note, be very careful with people who promise to help you for a fee. Those companies are for profit and offer the same service a non-profit agency would offer. HUD has a list of local non-profit agencies that can help you.
Sorry if this is lengthy, I just have a lot of information about the subject. Best of luck to you and your family.