To the extent you can prove the commingled funds originate from you, those funds are protected. However, medicaid eligibility is determined by need and a spend down of assets is going to be required beofre your mother will be eligible. In other words, she will need to spend her own money before medicaid will contribute.
The rules are fairly strict and there is a 5 yr look-back to preclude people from protecting assets by giving them away right before they apply for medicaid.
However, there may be certain tools to utilize to maximize the available asset protections under the law. Be aware, though, that at 87 you are a bit late to the game for asset protection.
In any event, it is still worth talking to an estate planning attorney to get all your options. If you need assistance finding local counsel try Martindale Hubble (site rules prohibit us from referring specific attorneys) . Many attorneys themselves use this site to locate attorneys outside their jurisdiction or expertise:
It is a huge worldwide database searchable by location and specialty. The attorneys are all peer rated. So, they represent the top of the profession.