When I say family plan, it is really just me and my two kids. We moved my wife to her own plan, through her employer, before we had our daughter, so that we would only have to pay around $4,500 out of pocket for the birth of our daughter, instead of the $8K+ that it would have cost us if she had stayed on my plan with our son. We just haven't moved her back. It all just seems a bit expensive to have to be $1200-2K out of pocket for a routine procedure that takes 20 minutes or so. Makes me concerned what it will cost when anything major happens.
I understand and have empathy for your situation, I have a few thoughts for you. I know most of the people who replied before me and they are telling you the truth, there is not much you can do. Add me and my 36 years into this mix and you have about 110 years of experience replying to you. Second, you are actually getting a good deal, not great, but good. Third, you are not thinking about this correctly. As Chazm said, insurance is for the big expenses. Lastly, ask them what their charges would be if you paid cash. You may find it to be cheaper. Good luck.