Me personally, I'd destroy it all. It's a plant out of place that is wreaking havoc regardless of whether it is a native species to the portion of the US where you garden.
I wouldn't screw around with planting it in by the other nasties to see which pulls down the house first. In our old house, I planted a few "gift" plants and trained them to the brick chimney. Thought it would be so romantic having vines scaling the south side of the house. Total bill for tuckpointing the chimney and that entire side of the house was around 10k. My husband was fit to be tied and said with friends bearing gifts like that... who needs enemies.
Are the stems of the second plant you photographed square to the touch by any chance?
Roger that on the morning glory. I tossed it roots up on the paths between my garden beds (I've mulched the paths with cardboad to keep down weeds, so now they double as a baking area for stuff I pull).
The second plant is round-stemmed, not square. Here are hopefully better pics of it. I have this thing coming up, literally, all over. If it's edible, I can quit worrying about the garden! Someone speculated in another thread (which I'll have to find) that it's shiso. I seem to have some purple shiso volunteering on one side of the house (there are herbs right where I'd put a kitchen herb garden, so I bet I'm not the first to think of that). And this looks a bit like it, at least in leaf shape. But I've now seen some itty bitty shiso sprouts near the parent plant, and they're uniformly dark purple.
Top view:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0163.jpg[/img]
Side view:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0162.jpg[/img]
Root:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0161.jpg[/img]
The second plant is round-stemmed, not square. Here are hopefully better pics of it. I have this thing coming up, literally, all over. If it's edible, I can quit worrying about the garden! Someone speculated in another thread (which I'll have to find) that it's shiso. I seem to have some purple shiso volunteering on one side of the house (there are herbs right where I'd put a kitchen herb garden, so I bet I'm not the first to think of that). And this looks a bit like it, at least in leaf shape. But I've now seen some itty bitty shiso sprouts near the parent plant, and they're uniformly dark purple.
Top view:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0163.jpg[/img]
Side view:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0162.jpg[/img]
Root:
[img]https://i287.photobucket.com/albums/ll138/crispwriting/PICT0161.jpg[/img]
Some sort of a Three Seeded Mercury? Acalypha? Acalypha virginica maybe?
Look at the veining only in this photo and compare it to what you have-
https://www.noble.org/Ag/Wildlife/DeerFoods/PlantPhotos/Photos-Large/C-028-02.jpg
Now look at all of the photos here and compare to what you have-
https://www.ppws.vt.edu/scott/weed_id/accvi.htm
The below is a pretty darn good site to check for photos of weeds for comparison if you have an idea of what you might have-
https://www.ppws.vt.edu/scott/weed_id/genusindex.htm
Unfortunately, their site doesn't have a key to be able to search based on characteristics.
Here's another really good site for photos however it has no way to search based on characteristics either-
https://weedid.missouri.edu/index.cfm
Here's University of California's photo gallery of weeds-
https://www.ipm.ucdavis.edu/PMG/weeds_scientific.html
This is a book I own that helps me out-
https://www.ag.uiuc.edu/~vista/html_pubs/WEEDS/list.html
I have lots of books but this one happens to be online. Note they have black line drawings. I like black line drawings better than photos personally.
This site cracks me up- Weed Alert
https://www.weedalert.com/
The U of I does have an online key for weeds but their photos aren't the greatest-
https://weedid.aces.uiuc.edu/
Our tax dollar at work here-
https://www.nps.gov/plants/alien/
We do have a fun site for Weeds Gone Wild's Least Wanted-
https://www.nps.gov/plants/alien/factmain.htm
Look at the veining only in this photo and compare it to what you have-
https://www.noble.org/Ag/Wildlife/DeerFoods/PlantPhotos/Photos-Large/C-028-02.jpg
Now look at all of the photos here and compare to what you have-
https://www.ppws.vt.edu/scott/weed_id/accvi.htm
The below is a pretty darn good site to check for photos of weeds for comparison if you have an idea of what you might have-
https://www.ppws.vt.edu/scott/weed_id/genusindex.htm
Unfortunately, their site doesn't have a key to be able to search based on characteristics.
Here's another really good site for photos however it has no way to search based on characteristics either-
https://weedid.missouri.edu/index.cfm
Here's University of California's photo gallery of weeds-
https://www.ipm.ucdavis.edu/PMG/weeds_scientific.html
This is a book I own that helps me out-
https://www.ag.uiuc.edu/~vista/html_pubs/WEEDS/list.html
I have lots of books but this one happens to be online. Note they have black line drawings. I like black line drawings better than photos personally.
This site cracks me up- Weed Alert
https://www.weedalert.com/
The U of I does have an online key for weeds but their photos aren't the greatest-
https://weedid.aces.uiuc.edu/
Our tax dollar at work here-
https://www.nps.gov/plants/alien/
We do have a fun site for Weeds Gone Wild's Least Wanted-
https://www.nps.gov/plants/alien/factmain.htm