Oh, but 'proper pronunciation' is such a mystery. I believe mine to be quite good -English pronunciation, I mean-. In my first week in Wales (out of 9 months), a Welsh girl in my Residence Halls took me fore another Welsh (from some small town far from Cardiff, I guess). When I told her I was from Barcelona she was so shocked. Then she kept telling everyone we met on the way (we were going to the cafeteria) that I was Spanish 'and look how good her English is!'. I was so embarrassed lol
This is something I can do: reproduce sounds I'm not used to. Imitate voices, and accents, my tongue, mouth, throat, nose and ears allow me to do that. Other people don't have that ability, but it doesn't make them worse non-native-speakers. You can't really help that, especially after a certain age. That doesn't mean you can't improve the rest of language skills up to perfection.
May I ask how old your children are?
I have a weird accent due to British, New Yorkian (does this word exist?) and Californian (with a tad of Honduras) influences. Plus, TV series and interviews I regularly watch. Sometimes I sound extremely British-posh, then suddenly I am this badass latino girl. Yes, there might be a bit of multiple personalities issue in the mix lol. So beware, if your children keep changing teachers -even if all of them are native- they might still sound weird!!
PS: We are so going OT here, but I can't leave a discussion like this go off lol Maybe we should start another topic or something?