This is only kind of a "problem".
If it is a problem at all, it is your DH's problem and not yours.
My in-laws, who I believe are fairly well off, have decided that as part of their estate planning they are going to gift a house, over the course of many years, to their four children. It is not their primary residence - it is a vacation home - but it is good sized. I think this provides them with a way to "gift" some of the value of their estate, while still enabling them to use the home, for the next ten years.
Their money, their house, their decision.
Three of the children live about three hours away from the house, and already use it regularly for weekend getaways. Two of the three couples are big earners - probably bringing in 7 figures annually. DH and I live on the other side of the country -- and, given the lack of proximity to an airport, it would take us about 10-11 hours of traveling, with multiple flights, to get to the house. We have three kids and a very tight budget. So realistically, we will almost never use the home when it becomes partially "ours".
First off, if your ILs are smart (and have a good lawyer), it won't become yours & DH's; it will become your DH's. He is their son. Whatever they leave, they will leave to him, presumably. Second - again, their money, their house, their decision. Your specific living arrangements are your concern and not theirs.
To some extent, it is what it is, the house will be an asset on paper, and while I feel DH is getting the short stick in the situation, his parents made this decision about giving away their money and it's their call. But, I'm kind of worried that this "gift" is actually going to cost us money.... I'm assuming that at some point we will be on the hook for a portion of the property taxes and house upkeep.
If your DH is concerned about this, he should talk to his parents.
Additionally, when the other families inevitably decide it's time to redo the house (and they will be right), I'm worried we will be expected to contribute 1/4 of the funding. Beyond the fact that we simply don't have extra $$ in our budget, it would be crazy for us to invest in this. FIL suggested maybe one of the other kids would buy us out, but I'm not sure what their motivation would be since they would have use of the house whenever they want it already.
Their motivation would be a larger share of the house (and therefore a larger portion of the proceeds in the event of a sale).
Anyway, what quesitons should my DH be asking and how do we approach this -- I don't want to appear ungrateful for this "gift" but if it actually is just a liability and a potential source of conflict with DH's siblings, I'm wondering if DH has a legal right to decline the gift?
Yes, of course he does.
Do we try to rent it out three months a year to cover our costs (no one would want that and I don't even know it would be allowed)? The family is communication-challenged -- there are never ever discussions of important topics. They just say things in passing and hope it sticks. So there has been no discussion of an ownership agreement, etc.
Your DH, his parents and his siblings need to meet with a good lawyer to discuss how to handle this.