An attorney or financial planner would be good to speak to, but here is what I can tell you.
First of all, any proceeds from the home should be tax-free, since it is your mom's primary residence and she has presumably lived there for more than 2 years. In most cases, profit is tax-free up to $250,000, but there are always quirks and exceptions to the rule. Consult a CPA or the IRS website for confirmation of this.
Mom's name should presumably be on the home if you are using her money and if she is going to be living there. A lot of suspiciousness will be raised if she is not. Believe it or not there are greedy kids out there who rob their parents blind and put them in a nursing home once they've gotten what they want.
As far as the mortgage goes, it's probably going to need to be in your mom's name or your sister's if she has income. To do a mortgage in your name, this would be classified as an investment property, and investment property guidelines would not permit mom to "gift" you the money for the down payment. So mom would have to qualify for the mortgage payment based on her Social Security and Pension income (plus any income from your sister assuming she is credit-worthy).
Now if mom can't qualify for the new mortgage all by herself then FHA allows the use of non-occupying co-borrower (you) income to qualify. Your credit needs to be acceptable, as does hers, and your income and hers combined must be enough to qualify for both your house payment and her new one.
I can walk you through the mortgage end of things and let you know your options. Then from there you can can speak to an attorney or financial/estate planner who can advise you on ways to make sure everyone protects their best interests in this transaction. Feel free to give a call with any questions.
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