You can get a VPS on Vultr for $5 a month that’ll be plenty for your use case. For security look into mTLS. Web servers like Caddy support it pretty easy. You put a certificate on you and your wife’s phones and only you will be able to connect to your endpoint.
They’re just hospitals. In fact they’re the biggest group of non-profit hospitals in the country. They are generally speaking a very good thing. The main problem as discussed here is their restrictions on reproductive care, which is a huge problem and should not be allowed. It isn’t even like to be employed there you must be Catholic, or even Christian.
If you couldn’t suss out the obvious sarcasm, it might be time to go offline for awhile and recalibrate.