I don't have easy answers. My father has gone through this with his family's rural property, and the house I bought went through a foggy period like this for 7 years with it's ancestral family before it went on the market.
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I personally think the family will need a real sit down to discuss what everyone's needs and desires are with the house. There's a lot of emotion wrapped up in old family homes. I also think after that discussion some real legal documents need to be drawn up. The trust should have someone who is overseeing the details and can act as technical owner if there is an impasse.
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Our family handled things by moving my grandmother's things out of the home and they were willed after her death. We made sure everyone had a say about items of sentimental value. We sold the house and split the sales amongst the children. Since you are not selling and are figuring out rent for potentially yourself, that's trickier. The cost of upkeeping older houses is high and the potential damage of the house if no one lives in it is higher. We had thousands of dollars worth of water damage in our house to deal with because the families had left it vacant. Pipes (from already "rustic" plumbing) rusted to the point of disintegrating, ceilings were damaged by moisture from the house being left unheated, even the furnace piping had water damage. If the house is paid off and you are paying the utilities and upkeep, I think you actually shouldn't be paying rent, as you have done the family a service by keeping the house in repair. As to how to state this without drama, I really don't know, it depends on how everyone gets along. But if you worded it like, "We can take care of the place for everyone and stay on at the old house awhile as DH has a near by job. Is there anything we could do for the house if we lived there?" If the house is in good enough condition that it doesn't need significant repair and upkeep, and the family feels rent is fair, then maybe you should base the rent on what others in the community are charging. It might take asking around as rentals are less common in rural locations, but they are there and there is probably an unspoken going rate. Then the rent could be shared amongst family. But in that case you shouldn't be left with significant utility costs (if it's cold where you live, remember old homes usually are less insulated and more costly to keep) and you shouldn't be the ones fixing the house.
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Also, you didn't say how used you are to rural living. I'm born into it and love it, but it can be a little overwhelming if it's not what you're accustomed to. I tried to prepare everyone for the move to the community more so than the house when we decided to move to our very rural location. We spent a few months coming to the house on weekends before moving in all the way and used time to meet neighbours and learn some local news. We planned for what sort of things we could do for recreation and made sure we had what we needed to make our own (for us: gardening supplies, wine making supplies, enough computer games for DH, kids joined some sports, started going to church just to meet the neighbours and now it stuck!).