Effect of MFS vs. MFJ on Medicaid trust (owned by one new spouse but not the other)

Context: Two years ago I married a woman who had (with her late husband of 63 years) set up a Medicaid trust so as to shield their assets from ultimately being eaten up by nursing-home expense (still hypothetical, but getting much less so). I myself do not have such a trust. My wife and I keep our finances separate (even keeping our checking accounts at different banks), but I fear that my unsheltered assets will now be counted against her and defeat the purpose of her trust, to the detriment of both of us.
Questions: Is my fear justified? Would filing as MFS provide some protection against that outcome?  (For us, the increase in total taxes would be tolerable as a price to pay for maintaining the benefits of the trust.  It was because of my uncertainty about which way to file [MFJ vs. MFS] that I ended up filing for an extension.)