Personally, I would not be so quick to get rid of the cat. How severe is your grandson's asthma? How long have you lived in the house? The truth is getting rid of the cat doesn't get rid of the allergans. They will still be in your ducts, in you carpet etc... Because of this, most doctors don't demand the pet be removed any more. Just kept away from the allergic person. Of course, if you granson's case is very serious, it might be a different story.
I don't have asthma, but am allergic to dogs. We bought a house that used to have dogs.(stupid I know) We had that carpet cleaned a number of times, vaccumed with a HEPA vaccum cleaner. But it didn't make a bit of difference until we finally paid the big bucks to get new carpet in the entire house. If you do decide to give away the cat, make sure it isn't in vain, your son and d-i-l need to replace the carpets, no matter how new they are.