An IUD is removed by pulling on it, thats why they have strings, that is literally the way they are removed.

By a doctor that knows what they're doing.

OP's husband is not qualified to remove an IUD. OP's husband was angry, which means he was probably far more aggressive than a doctor who has calmly removed thousands of IUDs with years of practice and training. OP's husband has none of that. You cannot possibly say that OP will be fine. Especially since OP was trying to defend herself while it was happening, who the fuck knows what he did in order to try and get it out.

Saying she will be completely fine is dangerous. She SHOULD go to a doctor to be evaluated to ensure nothing bad happened. Could he have taken it out without damaging her? Possibly, but a DOCTOR who can physically exam her should be the one to judge that.