I'd talk to your SIL. I have the exact same dietary restrictions as your DH, and the turkey is one of the few things on a typical Thanksgiving table that I *can* eat. Spicy doesn't bother me, but my BIL never could take lots of pepper.
My family's solution is that we fry TWO small turkeys, one with the Cajun injector, and one with a simple broth injection; it never fails that both get devoured. Also, one of the key items to try to include would be some steamed veggies rather than the typical casserole-style that normally shows up at Thanksgiving. Also, get some packet gravy; it's normally fat-free, and you can pop into her kitchen to mix it up in no time (gravy is another possible source of his digestive distress, because homemade gravy normally has a ton of fat.)
As long as your DH is eating white meat cut nowhere near the surface or carcass of the bird, then it isn't the frying itself that is causing the problem, because there is almost no fat absorption at that area. What it might be, however, is a reaction to the oil being used, depending on what's in it. Frying oil is very expensive (normally about $50 for enough fresh peanut oil for a 14 lb. bird), so it is often reused, and it definitely absorbs and intensifies spices.
Talk to your SIL about how you'd like to accommodate your DH' medical issues without having to skip the family party. (If he has been really ill, the odds are that quite a few people are concerned about him and would like to see him.)
Offer to help her cook so that the extra stuff isn't a burden.
(And if they like Cajun turkey, buy some Andouille and French Bread as a gift, and put the carcasses and leftover meat into a crockpot when dinner is over; because Black Friday Gumbo is a modern Cajun tradition.

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