Town bike intermittently harder to pedal I have a Dutch town bike with backpedal brakes (omafiets). I live in Amsterdam where it's flat and have checked the tires are fully inflated.

Originally the bike was very easy to pedal and often it still is. However, sometimes it feels about 20-50% harder to pedal. For example, flats feel like small upslopes and long upslopes feel intolerable. I'm trying to account for the slope, wind and my own tiredness. Occasionally it feels like I turn a corner and it's suddenly easier or harder. I'm often doing the same routes with different perceived difficulty.

My feeling is that something is sticking on the rear wheel. I have occasional perceived a small dragging sensation whilst pushing the bike with my hands (dismounted). My assumption is that the brake is slightly sticking. Two different bike shops have told me that this isn't possible. There is some slight side-to-side play in the wheel (about 1-2mm at a guess).

First bike shop said it would be the side-to-side play, second bike shop agreed so I had them fix it. They replaced the chain, pedal attachment, rear wheel and rear axle at significant cost relative to bike value. This did not help. Recently went back and they said the wheel is loose again, suggest tightening again. Of course, I'm doubting this is the problem.

I've read that cone adjustment should be done in this situation. However, my understanding is that tightening the wheel will actually make it harder to pedal - the adjustment is a trade-off between ease of rotation and stability of the wheel. Do I understand correctly?

Any other ideas on what could be causing this?
Are you sure you don't have a kick shift/kick back hub in the rear? I had this exact problem after I bought a new, used rear wheel for my town bike. 

Seemingly at random it would be much harder to pedal, sometimes forcing me to hop off and walk up hills. At other times I'd be able to ride up the same hill! I thought I was going mad, and I too thought something was broken.
After a while I noticed a pattern, that it was changing in "difficulty" whenever i braked, ie. backpedaled. Now I love it, easy, hands-free shifting!

Sheldon Brown glossary page: http://www.sheldonbrown.com/gloss_i-k.html#kickback