You really need to see an elder law attorney to plan for your mother's eventual (long away, we hope) passing. There are consequences that go far beyond taxes.
Briefly, the legal and tax situation is she would be giving you her 1/3 share of the home (1/6 to each of you and your spouse unless you word the deed differently.). The gift itself is not taxable (unless her estate is worth more than $11 million), but the gift may change other tax and financial situations.
First, you may pay more capital gains tax when you eventually sell the home if 1/3 of it was a gift from your mother, whereas you would pay less capital gains tax if you inherited it.
Second, if she requires residential care for a long term illness, Medicaid will only pay after she has spent all her own assets. This could mean she has to sell her 1/3 ownership share, which would force you to sell the house or buy her out. If she has made large gifts within the 5 year lookback window before she goes into care (like giving you her 1/3 share), Medicaid can require those gifts be used to pay for her medical care before Medicare will take over. (This can be very complicated--your mother would not be forced to sell the home if the other owner was her spouse who will continue to live in the home after she becomes a patient at a nursing home, but I don't know if the same rule applies to children living with the parent.)
It might be wiser for all of you to change the deed to joint tenant with right of survivorship, or to give your mother a life estate. This can vary from state to state, but it may reduce the capital gains tax when you sell. You might also consider putting the home into a Medicare Asset Protection Trust. The trust owns the house, so that Medicare can't force your mom to sell her 1/3 share to qualify for Medicaid if she requires long term care. Then you would inherit it from the trust after she dies. (The trust can be dissolved if you want to sell the house and move somewhere else, but if you put the new house into a similar MAP trust, it starts a new 5 year clock on the lookback period.)
Of course, these ideas would probably affect your refinancing options. Are you being forced to refinance for other reasons, or can you put a pause on this until you talk to an Elder care attorney/estate planner? They may have more insight than a general real estate attorney.
Good luck.
