A reverse mortgage will not work if she is moving away to be closer to you....reverse mortgages are for primary residences. She would be able to finance another home if her credit is good and her income can fall within the correct debt-to-income-ratio for the loan she is applying for. She has some options....first does she want to sell her exsisting residence? If so, what is it worth in today's market and how long will it remain unsold? She could rent it out, but then she would be better off finding a real estate company that will handle the renters from application through payments...there is a charge for this and all rental management companies have different fees...so look around and ask for referrrals from other land lords.
If she has great credit, income, and assets...I would recommend a conventional type mortgage with a higher downpayment to lower principle balance. If she wants to retain as much of her savings as possible, a FHA loan is the way to go there. She should consult with a real estate agent in the area she wants to move to also to see what is available. A condo might be better suited for her also since maintence would be covered, however there would be maintence fees to consider. Either way, a lot of planning has to be done to address this situation...I wish you and your mother the best and hope everything works out.