Car Loan Financing

Can a credit union force car insurance on an auto loan after financing has already been established?
They tacked on an additional @$2700 onto my loan and since that time my car payment went from $350 a month to $700 a month. Before this happened, my credit was good, and since after that time my credit changed drastically. I’ve been told that this may be illegal. If anyone has info, please let me know. Oh, and this is in CALIFORNIA.
Thanks!
If you let the full coverage insurance drop on your vehicle? They do have the right to do this it’s called “Forced place insurance” the auto loan companies have been doing this for years.
The only way to get it removed is to get your own insurance and then prove to your credit union that you have insured the vehicle.