Equity in an inherited home?

My parents have set up a limited partnership, and in it I have inherited a $200,000 home that is completely paid for. My husband and I are 35 and want to build equity. The conditions of the inheritance state that if we move, we cannot sell the house; it goes back into the trust. If we move into this interited house, is it possible to build equity or gain equity from it? We currently live in a home that my husband's parents own. But, we would like to start building our financial futures. Besides not having to make mortgage payments, is it financially advisable to move into a house that may not allow us to build equity?

I'm a little confused by this part of your question: "may not allow us to build equity?"

Since there is no mortgage, you already have 100% equity. Moving in won't change that. If you're looking for liquid equity, then you can take on a mortgage or a Home Equity Line of Credit (HELOC).

I'm not sure what your question is, so I'm sorry if I didn't answer it.