Keeping this quick because I am ill, my house is full of squalor and I have a dinner party this week, ugh. I'm sure there will be errors in this post.
I try to avoid correcting my children, although I do expect them to learn by my example, and speak a fairly standard English. Correcting people's english is a) pointless and b) rude. I do expect my children to grow up speaking something like RP, as that's what their dad speaks, and that's what the teachers at school speak.
I do think there is such a thing as incorrect grammer 'I wanna go toilet' is incorrect, afaik there is no dialect that includes that construction. Of course 'we done that' is correct dialect - it is just a dialect that conjugates 'to do' differently. If you're speaking that dialect, you can't just say 'we dided that', can you.
The irregular verbs change conjugation regularly, and have through the ages. They generally become more and more regular. In time we may lose all of them (hurrah!).
Yes, 'standard' english is a class issue. Obviously the dialect that is branded 'standard' is the posh one. And women are generally more aspirational than men, and eager to have their children speaking 'properly'. This is an understandable desire - but it is a matter of class aspiration, not grammatical correctness, let's be honest here.
And as for the whole idea of not having different dialects! Come on, nobody talks the same way to their friends in the pub, the GP, their boss, and their mother. Everyone uses different dialects and speaking styles for different situations! You just have to learn how to pick the right dialect for the situation.