I think I have to side with your DH on this one. Going for a walk may actually help. And it may help you with your energy levels too (a decent paced walk, not some powerwalk see how fast you can get it done pace).

When you're pregnant your body produces a whole heap of hormones (these can be blamed for just about everything that happens to you during pregnancy). The role of some of these hormones is to relax ligaments and muscles to allow your bones and muscles and whatnot to move to accommodate the growing baby. A side effect of this is that it slows down a lot of your involuntary muscle movement. (think Acid reflux and constipation) In your intestine, this muscle movement is what causes your poo to move through and eventually out. The longer your poo is in your intestine the more water your body absorbs out of it and conseuently the harder it gets....hence constipation.
When you go for a walk, the movement of your body can help push your poo artificially through your intestine, so it can actually help with constipation (not all the time, depends on how constipated you are, but it certainly couldn't hurt to try).