You mean "Medicaid" not "Medicare," right? There are ways to navigate the Medicaid waters so I think it might be worth your mother-in-law's and wife's time and resources to consult a good elder care lawyer. For the most part, I think the income from this Lifetime Trust will be an asset or resource that will be counted for Medicaid eligibiilty; you should inquire with your counsel about whether this Trust would be recognized as a Qualified Income Trust for Medicaid purposes, in which case, the income might be distributed in such a fashion that it might not exceed disqualifying levels of income/resources for Medicaid purposes. Regarding the corpus/principle of the trust, what does the trust instrument say, I think is the short answer to your inquiry of whether the principle can be invaded by your mother-in-law (and thus Medicaid for resource counting)? If your mother-in-law has no claim to the principle, then it would stand that this can't be counted as a resource for Medicaid purposes.
Typically, the biggest asset that people need to take into account for purposes of leaving something to children is the house; you might have greater flexibility under Medicaid, depending on the State your mother-in-law resides, to deal with that asset in an appropriate fashion.
Someday this war's gonna end . . .