Mary:
I have a similar problem. My day tends to be somewhat condensed because of it and I've had to turn down some social invitations because I really just needed to get home and rest.
But you mentioned you get weak if you rest....I get a type of weakness that gets worse if I rest, and that I can sometimes walk off. I usually get this when it's been hot. If that's the case with you, you might try turning on the air conditioner, if you have one. You also might try resting for a bit and then going for a brisk walk to see if you can walk the weakness off. The ability to work the weakness off seems to be a common trait in people with Becker MC who have MC related weakness, though I get some forms of weakness that gets worse with movement.
You should also have some blood work done, as it's possible your fatigue and weakness might not be MC related. Have them check blood counts, iron levels, your thyroid, and for other things that could make you tired or low on energy.