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A covered employer must grant an eligible employee up to a total of 12 workweeks of unpaid, job-protected leave in a 12 month period in order to care for an immediate family member (spouse, child, or parent – but not a parent “in-law”) with a serious health condition.
This is normally meant for an illness. Now, you are asking to qualify to help give your wife fertility shots. This is pushing the envelope a bit since you are not really taking care of her per se - she is traveling. She is not ill. And unless you are a nurse, then it is unlikely an argument can be made that it is reasonable to only use you.
Ergo, I am afraid that this would be a very long shot to qualify under FMLA. You can get her doctor to write a letter explaining that only YOU should go with her and for whatever reason, only YOU are qualified to give the shots, and her pregnancy is a DANGEROUS one (thus qualifying under illness, perhaps).
Even then, it is up to HR of your employer to decide. If they deny it, you can sue in court, but it would be a very weak case.
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