*HUGS* If going home a different route takes care of the kid issue, I say go for it. It's really no different than avoiding pot holes in a sidewalk or a yard with a vicious dog. It's not letting them "win", because all they're after is to irritate you and alleviate their own boredom. You're not their entertainment. Let them find their own elsewhere.

Stress and age can both affect how a period looks and feels. What you're describing isn't abnormal in and of itself, even if it's nothing you've had before, but going to the doctor just to be sure is a good idea.

As for the rest, I know there's not much that can be done or said other than I'm pulling for you, know that all of this is really rough and a lot to try to juggle/handle while raising a toddler at the same time, and think you're doing a remarkable job of keeping it together in the midst of the maelstrom. I'm so sorry you're going through this. *BIG HUG*