Our Chewie is a little wriggle bug when we get home from work and let him out of the crate - so I can understand your concerns about your daughter capturing him, harnessing him, and leading him outside.. But I do urge you to look through the forums and read up on reasons that your Yorkie should not be left unsupervised in a harness, collar, etc.
We struggled with a figure 8 harness at first (we were new Yorkie owners, and didn't know any better!) Then we went to the step-in harness, which was FINE aside from the fact that it took time to get our little wriggler into it - as he would wriggle away and we would waste a lot of time trying to keep his hair from getting caught in the cliips...
Anyhow, we DID wind up buying a new harnessing solution from another YorkieTalk member - Brooke. We purchased a leather step-in-harness-leash-combination. It is FABULOUS! When we get home all we have to do is clip Chewie's collar on, have him step into the harness, and away we go! I know that I posted some photos a while back, and I've never linked something inside of a post, but I'll give it a try here:
It's hard to see his new harness - but here are the photos I posted.
We have seen many Yorkies quite happy in the Puppia harnesses, and have thought about purchasing one for Chewie - but I don't think that it's really his "style" right now - he's not a real sporty dog!
So, I wish you the best of luck on the quest for the harness! Maybe spending some good time with your daughter showing her how to calm down Lex when she gets home... Nothing will be an overnight solution, but there will certainly be many baby steps...
Chewie and Christina