chico I love your gardens! I had some of that purple stuff too it was called transdentia or spider wrot and I didn't like it either. I kept pulling it out and it kept coming back. I still think I have some! And I found some engleman vine in the backyard wrapped around my shubert cherry tree!
I'm going to have to get out there and get rid of it...again. LOL
chico about the peony not having many flowers it might be too deep, try scrapping away some of the top soil and see if that helps next year.