When I was a little girl, my father was the one who took me places. He always took me into the men's bathroom. The reason being that it is better for a little girl to be in a men's room than a grown man to be in a woman's room. I was always safe, since my father was always with me.
I don't see what is wrong with taking a little girl into the men's loo. It certainly didn't affect me negatively.
By the way, I had no idea that there were actually laws against going into the opposite bathroom. I thought it was just a matter of courtesy. If there is a long line to the women's room in a restaurant or at a show, I will sometimes use the men's rather than wait, but I will always knock first to make sure it's OK. I have never had a problem.