Carmen - I'm with you 100% (or more) on this one. My (late) mil used to always thank both me and dh for her Mother's day (or Mothering Sunday) card, and I used to say that it wasn't anything to do with me, rather that it was between dh and her. Not to be hurtful, just to say that it was a day between them, iyswim. Later on, she used to insist that she was my second mother, and then I was happy to be thanked, if that makes sense.
For my mother, it always had to be a Mothering Sunday card, and when I was younger, it was a special service at church, with a card and a small bunch of daffodils. I can remember feeling very embarassed going up to collect them from the vicar.
Perhaps you could say that you feel it's 'inappropriate' to send one, and that you are not going to send them to your parents from ds because the fact that it's inappropriate makes them feel uncomfortable, which as you love them it's something you don't want to do.
As for gp's day - well, by the time we had dd, we had 1 parent between us that we didn't see. Mine were long dead before gp's day cards were even dreamt of, and so were dh's, so the problem didn't arise.
As for my parents and pil's I don't think any of them would have thanked us for either cards to gp's on Mothering Sunday/Father's Day, or for cards from an in-law on those days, either.
I've just had an evil thought - you could always lay in a stock, and 'by mistake' get them mixed up, so that mil got a Father's Day card, and fil got a Mother's day card. You could always say you bought them for the picture or something.
Good luck with presenting your dh with logic, it might be worth finding out why he's so confused about the boundaries.