Is it inappropriate to hang with a 40 year old mom and her 11 year old daughter, when I'm an 18 y.o. male?

I'm an 18 year old male and I get invited by a 40 year old mom and her 11 year old daughter to play cards and tennis and watch movies with them. They are my best friend's neighbors and have always been a family to him, and now I consider them my family as well. My parents think it's inappropriate to hang with them. I at first thought that they thought of the mom as a pervert, but she told me and my friend that she is very loyal to her husband and would never do such a thing. My parents want me to hang with guys my own age, even though I already hang with at least 40 of my guy friends very often. I want to be a role model for the 40 year old mom's daughter but my parents think differently. They think there's a relationship igniting between me and the daughter, but that's not it. I think of her as the sister I never had. I'm an Eagle Scout and have always made good decisions, and I believe that being a role model is a good decision. So is it still inappropriate to hang with them?