I can be reached at 585-721-9857.
Keller Williams Realty
Century 21 Princeton Properties
However . . .
Your mother does not have to be on the new mortgage. If you and your husband qualify, then the two of you would purchase the property. Your mother would be a tenant in your property. However, that's also something to discuss with her. Would she be willing to go from a home owner to a tenant?
As for how to handle the equity in the two properties, check with an accountant. The main hurdle is how to transfer your mother's equity to you--presumably as a gift--while minimizing any taxes. There may be other ways, as well. But you have to look into that before you take any steps regarding sale of the properties or purchase of a new one.
Hope that helps.