The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at the Trope Launch Pad.
This is a bit specific - and vague at the same time. Let's break it up.
The husband is convinced vaccination will (or at least is likely to) harm his child. The best trope I can fit is Artistic License – Statistics (Projecting From a Small Sample Size - side effects are fairly rare, but they do occur, and he's deciding about his child's health, so of course the guy's biased; illness is actually more likely to harm his child, but he has not seen children harmed by illness, he's seen one harmed by vaccination, so Psychology Tropes might have something - we don't have epistemology tropes, alas, but this is definitely a bias towards what he's seen and experienced against what is abstract for him).
Because of this belief, when his wife has the child vaccinated, he sees her as a bad mother: Maternally Challenged or even Abusive Parents
Which triggers his Papa Wolf instincts and he decides to take his kid away from the "bitch".
This level of difference on fundamental matters may indicate a relationship that has been dysfunctional from the very start (they never talked about it? before it came up?) so I'd search around Grief-Induced Split (not it, but might be inspiration), This Index Broke Up or Psychology Tropes - in any case, it's hard to tell without a lot of details, like how was the mother convinced? why did they not vaccinate the child in the first place? (was it a decision they made together or did the father force it?) and so on.
It's definitely not a Toilet Seat Divorce, since the issue is real - it's about trust between the spouses.

Assuming the husband is telling the truth, and ignoring the controversial question of Artistic License – Medicine applying, are there any good tropes for the following?
A couple have refused to vaccinate their child because the husband's niece had serious side-effects from vaccination. Their child gets hospitalized due to what looks like it may be polio, but isn't. The doctors try to convince the parents to vaccinate their child; the mother asks them to do it, and when the father finds out that she did, he is angry at her and it's implied that the couple will.soon get divorced.