It all depends on the mare. Most (IMO) breeding calms them down, after the foal is weaned. (sometimes their "wilder" right after they have the baby, until it is weaned) But not all, I have heard others complain that it makes them "crankier". With all the overbreeding there is, I certainly wouldn't breed a mare just to calm her down though. Age and maturity usually does that.
I think adjusting the diet would be easier than having a foal. I used to have a mare that had hard cycles and a severe "moody mare" problem during certain times of the month. I started feeding a supplement called Mare Magic. Its an herbal additive and it really seemed to help her remain more "normal" all month long.
Yep, breeding doesn't always make a mare calmer. Think diet and training would play a more important role. Hey, thanks for the tip on the mare magic. I see that Smartpac carries it in addition to moody mare supplements.
I too, have a mare that is a handful that I intend to breed, but not for purposes for calming her down. I think it's best to get her under control with diet and training before I attempt breeding. Ya know, double the trouble. Yikes, that wouldn't be good.