Maudy, your DH sounds like he was cut from the same cloth as mine. We have a 3 yr old DS and 8 month old DD and ever since DS got to the age where he needed exercise (we have no garden but live next to a park), it's caused friction.
Basically, I find going to the park and pushing DS on a swing pretty boring too, but I think actually, that's what you sign up for when you become a parent: doing things some of the time (OK, a lot of the time) that you either find boring, or at least wouldn't choose to do on your own!
DH NEVER volunteers to go out and do anything with DS unless it's really obvious I want him too, and I'm tired of feeling like a nag so I do it all myself. Yesterday I enforced a family walk to a big park in the morning. In the afternoon some friends were taking their kids to the swings and asked us to go - when I mentioned it to DH he said "Well I'm not going - I'd rather stay and read the papers" When I said, well actually, so would I, but since we have 2 children, how about thinking of their needs?, he just rolled his eyes so I left it and went on my own.
I agree that children can be spoiled by the idea that they have to be constantly entertained, but ours are still too young to go out on their own, or even play alone for very long, and yet DH just sits and reads his paper or watches TV. If I leave him with the kids, the TV's on full time.
It depresses me no end and i'm actually thinking about leaving as our views on childcare, as with so many other things, seem diametrically opposed.