Getting two cats caused some discussion in my home early in the marriage. 2750% of that would be a serious problem.
Never let your wife and kids look for a cat "on-line." The pictures are just too cute and they will "land" on a cat before you actually meet it.
So if it's sick, it doesn't matter. They already love and have bonded with the cute cat they saw on-line. It doesn't matter if it's allergic to itself, they will have to have it. Oh and when the shelter says take his sister too, you'll have to do that, because they love the cat.
Of course my revenge is both cats love me the best and will sit on my lap, eschewing all others.