If they do learn a language from you, it will most likely be diluted like the way you describe it. I think it's a generational thing, a result of being immersed in a culture such as the the US. There's little opportunity to use the language, and as such, it falls into disuse.
My parents are from mainland China and moved to Taiwan early on. I was born here. Even though my parents talked to me everyday in Chinese, my Chinese is conversational at best.
I think I actually learned French better from high school. At least I can read that.
I once met a Japanese friend's parents and attempting to impress them, I greeted them in Japanese. Her father replied in perfect English, "I don't speak Japanese."
