You should have no problem completing one of your concerns: transferring the deed into your name. Visit your attorney to have a new deed prepared and transferred, along with the appropriate conveyance forms, or whatever forms apply in your area. I would inform your bank that you intend to make this change. If this is your Mother’s primary residence, discuss with an attorney the option of granting her a life estate, or some protection for her should something happen to you, if that is in your plans. As for your other dilema, I agree with your assessment. A refinance with only unemployment income is going to be difficult. It sounds like you would qualify otherwise, as you have been keeping your payments current. I would approach a loan officer at the bank you have the mortgage with presently and see what their policies are for income requirements. If that option fails, try a local community bank in your area that may have a different policy in regards to your source of income. Honestly, though, I think your best option is to work with your present lender, as they are already servicing your loan. Good Luck.
It is highly doubtful that any lender (your current servicer or new one) will qualify you for a refi based on unemployment income as it will not continue for 3 years AND is more than likely not adequate for you to meet debt ratio requirements. You have a better chance of winning the lottery than getting a loan done with only unemployment as income. Please don’t get too excited about the possibility of doing anything until you start the new job.