I'm probably not going to be much help at all here, but let me see if I have the facts straight and then I'll through my 2 cents worth in
Are Alyssa & Jaelyn half sisters? (have the same bio-father?) or no?
My first thought was that if Jaelyn is a double Delta F508, you and Jeff must both be carriers, which would mean that Alyssa stands a good chance of having one Delta F508 gene and possibly another CF gene from Kim.... so the sinus issues could be CF in Alyssa as well......
You are probably going to tell me that no, Jeff is not the bio father of Jaelyn and that would blow my theory
Anyway....regardless of the possible genetics involved, my other thoughts are:
1) Kim doesn't have a choice - if there is a child visitation agreement in place, she has to send the kids over to Jeff or else she will be breaking the law.
2) If Alyssa has that many sinus issues, it may not really be a matter of Alyssa always "catching something" or "being sick" -- it sounds more like a chronic condition that should be addressed by her doctor and allergist. If she has had surgery on her sinuses, there must be a treating doctor involved somewhere.
So I'm thinking that rather than approach it from the angle of "I'm trying to protect Jaelyn" (which, I totally understand and would feel the same way about) .... maybe you would be more successful with approaching Kim directly with more of an "I'm concerned about Alyssa's health and comfort" to see what is/can be done to clear up her sinus problems. I know my son had a terribly snotty, ugly green goopy nose at that age too - a series of allergy shots really helped.
And if there is any possibility of Alyssa having CF, she should be tested.
Best wishes - I know you're in a tough spot, but the only solution here may be to cut out the middle man (Jeff) and work on a solution mother to mother