After some more practice I manage to solve the problems from my original post.
From time to time I have to transpose to be able to sing a song, and I also change single chords as I see fit.
Many of you guys will frown I know, but most important is, my son and I have lots of fun. He also does frown from time to time saying that I'm not doing things what is supposed to be done. He had some professional help and he think I'm a bit weird doing the things I do my way. My son tries always to play in the spirit of his teacher. As he did learned it a few years back, he's 'stuck' with the musical 'laws'. But hey, that's my opinion.
Point is, we do have fun playing together. Many times we have to compromise to be able to play together...
What's more, I even can find the proper cords for a entire song that I can sing, of which no chords are available on the net. And after a few days of struggling with my guitar, playing such a song to my son he's pretty impressed. He knows how these songs should sound like because I used to sing these (local) songs(without a guitar) when he was little.