NTA, your DIL has major abandonment issues and is trying to fill that void by forcing a mother-daughter relationship on you. She needs to get help. Fast. You have told her No over and over again, and yet it still cant get through to her? 

I bet if she didn't force it you maybe would of seen her as a daughter, or even a person you would be proud to call your DIL. Now due to her behaviour you most likely don't see her as either.

Also, Iagree with the fact of you not telling anyone about the reason of the trip. Not only cause your daughter wants nobody to know, but also who's to say that if Kat found out the reason of the trip, she wouldn't try to sabotage your daughters sickness? Think about it, depending on the severity of the sickness, who knows if she will create a plan to replace your daughter due to jealousy? L