The relative still doesn't need to know you'll be gone for two months...

They can be lead to believe your visit and their visit, is about the same length and at the same time.

No need to say, "oh my wife is not here she will be back in a few months because she's ill"...

It's just none of their business and there's really no reason to invade your privacy, unless the relative was going to be around for the duration of your absence.