If you are receiving public assistance that limits your resources, inheriting property valued at $100,000 will make you ineligible. If you choose to use the money to remodel your house,
that does not negate the fact that you received an inheritance. You can do whatever you want with the money, but you will not meet the elgibility rules for the special assistance.
Are you sure that your joint assets have to be at $3,000 or less? With Medicaid, there is a Community Spouse Resource Allowance that allows the non-Medicaid spouse to keep more than the Medicaid-eligible spouse. I don't know which program is providing the assistance, so this may not be the case. If both of you are receiving Medicaid, then this number makes sense.