I don’t think any dental plans cover braces, do they?
As far as pulling teeth, I am not sure, but overall dental insurance sucks. My aunt pays $150 a year and that supposedly sets the price for some of the work she has done, but I have my doubts about the plan. I think she probably could get the same prices without it. I pay out hundreds of dollars for her dental work. I can try to find out from her what plan she uses, I don’t remember. Since you say pulled, I am going to assume the teeth are already out? That should not be widely expensive I would think. If they are below the gums still, that is a whole different matter.
If you have a favorite dentist I would talk to the billing person and ask her to recommend a few companies, or ask the type of deal you can get if you self pay.
Also, if there is a dental school near you they probably provide free dental care, but then your kids will be the patients they practice on. It is all supervised of course. Often, using a teaching school means you have to go into the dentist multiple times when a regular dentist could do it in one shot, so it takes some patience. What I don’t know for sure is if they allow children to be the guinea pigs.