The vaccination thing is complex.
Your options are to allow the few that work
MMR, DPT, reubella, polio. And maybe smallpox although thats different. All the illegals are carrying these things and these basic vaccinations have demonstrated that they worked well for 50 years without any real problem .

Do not allow more than one single injection per week, preferrably 1 per month. Never while the child is sick.

Ignore the other bullshit injections, they are not needed for normal people.

If needed research the immunization for how its made and if possible claim that what its made from is an allergy, like flu vaccine made in eggs so you can claim an exemption based on allergy. Be aware that there may be alternatives.

You can probably bribe some minority inner city pill mill doctor for a reasonable price.