It sounds like you all are dealing with a potentially very serious problem. I sure hope the house move thing goes well.

So far as plants go, it sounds like you'll have to stick with either plants that can deal with soggy soil (there are actually many that can), or, build raised beds/berms. Trees (at least the ones that don't like "wet feet") will require relatively large berms. Botanically speaking, your property probably has as much potential as any other property, but you just have to select the right plants. You'll be able to grow things that many others won't, just as it may be more of a challenge for you to grow some of the things that might do well in a drier sites.

Wet weather springs are another name for it. In August your land may be hard and dry. That might perhaps be a better time to think about moving your house.

I did a walk around the back couple of acres here yesterday, looking for new border locations, and found more than I remembered of wet areas that logically should have already drained off from the previous night's rains. The pond we have in springtime was full (two identical trees growing out of it, I know not what, submerged to about 30".) That pond is totally dry in August. Still, I keep swearing I'm going to put goldfish in to keep down the mosquitoes. Don't know as it will do a lot of good, seeing as how there is enough standing water from the other artesian springs to keep the critters spawning. I put in my beloved cardinal lobelia about 4 years ago just down slope of one spring and they have all disappeared. (Just could have been the pine tree that came down on top of them.) Anyhow, for one reason or another the area has been neglected over the past 5 years and small pines have found it a happy breeding ground, as has wild roses. I'm going to try sedum in some of the wet spots - nothing kills it, and in spite of its succulent appearance, I've had luck with it in wet spots before. Rose of Sharon, Cardinal Lobelia, astilbe, goat's beard, Leatherleaf Mahonia (which Brandon tells us in invasive here in
Tennessee) and sweet woodruff have all flourished in wet spots for me. The question is will they do well when the area dries out.

The old timey solution for (too) wet areas was planting willow trees.

Or, put in a muscadine grape vineyard-and make money from the resulting heavy crop.

The water under the house is still high and when I pulled the pole up from between the pea plants to support a cover for the only warm weather plants we have up it came out with a sucking sound and water ran out of it. My husband dug a hole in the ground and it remans full of water. So for this summer I am using it to water my beds both flower and food plants. I just dip a small plastic bucket in there and use the water that comes up. Feels more and more like home here as we lived in marshy land in my childhood where we had a fence around a three foot square spot that was quicksand. I remember trying to find a branch long enough to not go all the way under and we never could. Muscadine grapes is something I will have to research as no one I know has ever grown them. Thanks for the follow up.

where in TN do you live? does the area around you appear wet? Neighbors yards?

Do you have a septic system or municiple sewer? An irrigation system?

My point is "are you sure you have underground springs or a high water table, and not something else?
Move your house? Ouch! Very expensive even if it is a "mobile" home.