Meditation for relaxation?

I went through the transcendental meditation program about 30 years ago. All I'm left with at this point is a mantra and the notion that I should meditate 20 minutes twice a day. But I've never been able to stick with it--when I was single the cat would bother me; with marriage, a child and fulltime work, I never found time where I wouldn't be disturbed. So now I'm trying again. Starting with 20 minutes once a day.

I've been at it for a few weeks--does anyone else have a hard time sitting still for 20 minutes? Or having one's mind calm down for 20 minutes? I seem to have more, disparate thoughts during those 20 minutes than at any other time. How to clear the gutter of snow and ice; what we need at the store; when will I need to walk the dog--you name it. The guidance is that when you notice that you have a thought, let go of it gently and return to the mantra. But it seems to take me a long time to notice that I'm thinking thoughts, and I'm only able to have the mantra (and only the mantra) for a few seconds at a time.

And then there's the posture--my lower back starts to hurt after a while (that seems to be getting better), and my legs get stiff, so I end up focusing on whether I can stay still or need to recross my legs and/or shift my posture. And I have yet to make it to 20 minutes without looking at the clock--my record was yesterday, when I first looked at the clock after 16 minutes. But then I looked at it every minute--didn't want to go past 20! Today I was back to looking at it when only 12 minutes had gone by.

So does meditation really reduce stress, like the studies say? Guess I'll see...