J.K.
I live in Wisconsin. Here there is nothing illegal about a child being in a bar with a parent or guardian. It's not uncommon to see families in bars for lunch or dinner.
I just looked up Nebraska law, and it is the same. As long as she is with a parent or guardian then she is allowed to be there, but she isn't allowed to drink alcohol.
My husband's father was a bartender so he spent a good deal of time in bars as a child, particularly after his parents divorced. When he was old enough, he helped to serve food and clean tables. He was not a problem child or teen, and as an adult he has a good relationship with his dad, a strong work ethic, and isn't much of a drinker because he knows what alcoholism does to people.
It's not the location that causes lack of boundaries and poor behavior, but the quality of the parenting. You're with a man with whom you have serious differences in opinion. Because it is his child and not yours, you don't have legal standing and will have to defer to him. You can only control your own actions and decisions. You will probably have to accept that things are now as they will continue to be, and from there decide whether or not you can live with it and be happy, or if you need to move on in life without him.