my mandevilla plants are flowering like crazy but no vines.
You may have a dipladenia rather than a mandevilla. It looks very much like a mandevilla but doesn't have the upward growth.
My dipladenia suffered through one 32 degree light frost. We brought them inside within a few hours; leaves dried up but soil not frozen. If we remove all dead leaves and cut back stems, will it regenerate in a 70 degree environment in a southwest window?
It won't hurt to try. You can check for stem damage by scraping off some of the stem. If it is green below, the stem survived, but if not, trim till you reach green stem. If needed, you can cut it all the way back to about 6 inches. Water sparingly for the winter and hopefully, you will see some new growth (may not regrow till spring).
It also shares a pot with wild violas that I have to keep pulling out as they run wild
Unfortunately, your photos did not come through. I am unable to see the pest in question. What I can do, in the meantime, these articles will help you to craft your own pest control solutions:
As long as you repotted it correctly, and carefully, it should be just fine.
What do I do for winter? Can I dig it up and repot?
I would keep it in a container instead of planting and digging up every year. This can get rough on the plant. This article will help: