From your description, I'd guess Virginia creeper, which is also called woodbine. It can be a rampant grower and would probably cover that fence in no time, but I might pass on it. It's in the grape family and has fruits that look a little like wild grapes, but I believe they're poisonous. I once bit one accidentally while picking wild grapes (they were growing intermingled). It was one of the foulest things I've ever tasted. Plus, the vines might soon become heavy enough to knock down the fence--they will take over and cover small trees, given the chance. Here is a link that might be useful:

The "tree" is Malva assurgentiflora and the climber is a Passiflora.

Everyone-- Thank you so much for all your comments and suggestions! They've been really helpful to start my new journey of...well, wondering what to do with this peach tree, lol! Since the last time I was here, there have been some...interesting developments with my Dr. Davis peach tree. Unfortunately, no bizarre midspring appearance of flowers, but leaves are coming in! As well as.... well, baby peach trees that are now pretty big. O.O See attached photo. I believe these little trees coming off the main tree are called 'suckers'? And are probably no good? This photo was taken a month or so ago. And now, these tiny suckers are nearly my height now, probably a good four feet! What should I do, guys? Should I cut down these suckers, take out this tree, give up? The funniest part of this is that these only grew from the weirdest trigger: my mom dumping all the ice from our freezer onto the peach tree. Maybe it was tricked into thinking it had a few more chill hours? LOL! Any suggestions would be appreciated, as always! miss hibiss

I didn't mean to sound like you tricked us. When I say staging, I just.mean taking the picture. In this case the original vine was either missing leaves when you came upon it, and you photographed it as it was. You didn't notice it had a leaf arrangement issue. I was asking you to try to dicern the leaf arrangement before you photograph the plant, and to stage it so us viewers can clearly see the leaf arrangement. In this case the more viewable parts of the photo showed what appeared as an alternative arrangement, and it was sketchy and blurry in the couple spots where there might have been opposite foliage, so we all assumed it was alternate. Unless the 1st photo really was Convolvulus arvensis.🤔 I asked you if the recent photos are of the same plant as in the original photo? There are 2 scenarios. 1. The original photo was Convolvulus arvensis. 2. The original photo was Funastrum cynanchoides that was missing some leaves. I never said you knew what the plants were before you post them. I don't think that. I may have said the photo was deceptively staged, but I meant that because the leaf arrangement threw us off the photo was deceptive to us, not implying that you were being deceptive. I'm just used to seeing high quality plant photos where every part of the plant that might be necessary for an ID is shown clearly. So don't worry. I enjoy your posts, and I'm glad you do them.