Should you work for them? I think this is a matter of personal conscience.
Under no circumstances should you stay in their house. This will seem like you are endorsing their relationship. They will most likely be very hostile to your attending Mass and practising the Catholic faith.
I am sure they mean well, but they expect that all people will support the way in which they have chosen to live. They will be harsh on you when they find out you are a Christian.
I think that you should avoid living with them at all costs. Not only will this be bad for your personal faith, but it will be seen as an endorsement of their lifestyle.
Does this mean we cannot respect them? Of course not. These two men need to be respected and loved, for they might feel a real sense of rejection through the Church. The attitudes of some in the Church understandably would offend these men, for they have built their whole lives on this relationship.
But, we should never endorse such a relationship. It does not come from genuine affection and under no circumstances can it be approved.
Hope this helps!