Jessica is a Bene Gesserit and is torn in her duties. I doubt the Duke would just roll over and accept Paul being killed.
I suspect Jessica knows the Bene Gesserit need to know if Paul is the Kwisatz Haderach. Jessica needs the Bene Gesserit on her (or mainly Paul’s) side. She has to let the Reverend Mother do this test. It is a door that needs to be walked through from Jessica’s perspective but I doubt it is one the Duke would share (and he doesn’t know the half of it but suspects something is afoot).
Indeed, in the movie (at least, been a long time since I read the books), Leto asks Jessica if she would protect Paul. She says absolutely, with her life. Leto says he is not asking Paul’s mother but asking the Bene Gesserit that she is. She doesn’t have a quick answer to that. As you say, what is not said says a lot.