Welcome to gardening in florida!
It will be hard if not impossible to get rid of the potato vine living here part time. I had it at my last house and I was out there (by the lake) every few days pulling and digging potatoes. Even a potato smaller than a pea can start a new plant! Just get as many as you can and try not to let them go to "seed".
The other plant is a balsam apple vine (goes by various other names) is somewhat easier. There is usually a main root...or many main roots and not too hard to pull up. They can also be control by herbicide unlike the potato. Again, try not to let them go to seed. I have it coming up in my yard from seeds carried here by the birds.

Both vines take an investment in time over a long period of time. There are no quick easy solution, no "one time" and forget it solutions.

Palms? Hmm, no rule about cutting them down. If they are interfering with the power pole you could call the power company and see if they want to do anything about it.

Hi Laura! Thank you for the info. We live in California and have taken on repairing the place in Punta Gorda. It's amazing how things grow! I remember years ago that palm tree mess was a nice little landscaped area! The palm tree is not a very attractive one either and has multiplied into quite a scary area. I actually think we need professional help. So I guess we can tackle it again when we go back in the spring!! Thanx again!

Monkeyhut, It sounds like you might need to hire a landscape person to come in monthly and take care of the palms, the air potato and the vines. Is the palm an areca? they can get out of control for sure.

Alternatively, you can move here fulltime. LOL! If I were out of my yard for 6 months I don't think I could find the house!

Hi Peachpaws! I would love to move to Florida full time and leave the rat race of Los Angeles forever. But for now I have to settle on a week every six months! :(

I believe the palm is one of those arecas. It has sticks poking out everywhere. As you can see I am a novice with Florida plants. I have managed to create a nice container garden, with lots of pots and what survived is nicely controlled. I just want the place to look nice when we aren't there!

I have a lawn cutting service and have found a handyman who will help with the trimming and clearing out. It's so difficult to get things done long distance. All suggestions are welcome!

I'm curious which palm it is. Arecas don't have the "sticks poking out" as was mentioned. I am thinking it is probably just a Sabal palmetto. A landscaper can strip off the old fronds, leaving the trunk smooth if you wish, or they can be cut short, leaving the trunk with a hatched look. I battle air potatoes myself each year since they spread to me from a neighbor's large lot behind my property. I just cut and/ or pull every vine I see which reduces them. When the weather cools and they start to form the tubers, I just collect every one I can find and throw them in the trash. I see less and less each year, and I hope to be done with them soon. You can just rip out the balsam apple vine by hand; it is nowhere near as aggressive as air potato. I actually think it is attractive.

Hello jkrup44! Maybe it is a palmetto palm. I will have to get it trimmed because it has turned into a jungle of it's own. I don't know how the air potato got there, maybe from the hurricanes? I don't see it around the neighbors. I think once I get the area cleared out I will be able to control it. Hopefully!

Air potatoes are a real pain in the neck. One thing I have noticed about them is that they do much better if they have something to climb. If one is coming up in an open area of the yard, you can simply mow over it with your lawnmower. It may come back a couple of times, but then it will finally die. They spread by dropping tubers (the potatoes). So it is possible that a stick covered with air potato blew into your yard during the hurricanes.