Pampas, congratulations on having a grandchild.
I think most of the answers to your post are grossly unfeeling, and I do hope you are not dreadfully hurt by them, but I am afraid you must be.
That said: this is the way new parents behave these days, if you go by all the many posts on gransnet from paternal grandmothers!
If you are feeling that your son is being unbearably unkind and behaving badly towards you, I can only agree with you.
However, you need to try and view this without letting your hurt feelings cloud your judgement.
LEAST SAID - SOONEST MENDED
Anything you say will be taken amiss and you might just find yourself banned from your son's home, so put up with all his silly rules.
As like as not, in three months time he will have adjusted to being a father and be willing to accept all the help he can get!
I am very sorry to hear of your serious health issue - please do remember that chemo is extremely harsh on your body and on your feelings, so is the nagging doubt that you might not live long enough to see this child grow up. Shove that nasty thought as far into the back of your mind as you can, or preferably right out of it.
Your doctors say you are doing well, and they should know.
A quite different point is that you should not run unnecessary risks of contracting any infections at all, as long as you are having chemo, or recovering from it. So visiting anywhere at this time of the year when coughs, colds flu etc. are going the rounds is probably unwise.
Give yourself time to get through chemo and recovery from it, and let your DIL tackle her husband if she too thinks he is being unreasonable.
As to the dog and cat issue - some people regard cats as cleaner than dogs, but honestly neither should be around a young baby. Leave your dog at home, when you go to visit your son and his family, and put dog in a different room to them, when they come to you. That solves that problem at least.
I hope this all sorts itself out, and that you are soon feeling better and able to shrug and say, "well, I always knew my son works himself into states at the least little thing, and having a first baby is not a little thing. I'll just let him get over it in his own good time"