Fruit trees not rooting

About 3 or 4 years ago we got 2 peaches and 2 gala apples. The peaches were not the same cultivar though I cannot remember now what they were. Both were in the front yard and an apple tree too while one apple was in the back with a crabapple in between.
One peach had some sort of disease and the leaves would look burned and fall off. We have since removed both peaches. One last fall and the other the spring of 2013.
Both apples don't seem to be able to anchor themselves in the ground. We had one supported for 2 years. Because with the slightest breeze it would fall over. We finally took that out spring 2013. It flowered beautifully and the leaves were great, but it should have been able to support itself better after 2 years.
We have the apple tree in the front left and it is starting to lean as well. It has a big trunk, probably just the right size for it's age, it flowers well and this is the first year we have let it fruit. We have had to remove almost all the fruit because of either disease, insect or birds. It is tall, around 7', and the leaves look good too. Though it does take a stronger wind to encourage the leaning. This tree has not been supported for a year and a half or so. It hasn't started to lean until this summer. What could be wrong?

What is your soil like and how do you prune? If you have dense or clay soil, when you plant the trees, you should dig a hole at least twice as large as the root ball and loosen the soil and amend to promote root growth. If you are planting potted trees (as opposed to bare root), trim the root ball. A potted, bound root ball will never grow correctly if not trimmed.

Most pruning guides for apples say to prune when dormant. This is true in some situations, however major pruning when dormant (like is done on young trees) can promote vigorous branch growth at the sacrifice of roots, especially if you have a vigorous tree to begin with. I find pruning in late summer (aug, sept) once new growth is finished for the year leads to a stronger trunk, earlier fruiting and better stability. These cuts do not promote excessive growth the following year, so they have some dwarfing effect on the tree. Cut in winter to promote branching or where you want growth. Over fertilization will also have the effect of promoting branch growth rather than root growth, especially high nitrogen and may delay root growth. Under-fertilization will stunt the whole tree including the roots.

Another consideration is the root stock itself. Some rootstocks (especially dwarfing rootstocks) will never grow sufficiency enough to support the tree on its own in windy conditions. It's recommended to have support for dwarfs due to this reason. If you know the rootstock you can look it up and find information about growth/disease resistance, etc.

Also, where you are located (UT), the soil in your area may have a high salinity or high mineral content which would cause the burnt-leaf look of your peaches. You'd need a soil test to know where to start.

When I planted them, I think it was clay but not too dense. It wasn't hard to dig in and get the right size of hole. They were so small when we got them bare root, that I don't think we fertilized with the exception of the one in the back. We had a soda syrup drum filled with compost sitting 1 foot away from the tree. We had drainage holes on the bottom and DH would soak it once a week. That area actually turned out very nice and almost sandy after a year of that. I could dig 3 feet away from the tree and see the effects of the compost drum.
The one out front has been amazing. The trunk has gotten bigger faster without the aide of any fertilizer that I can recall. I have used BT around the root ball though. I have not trimmed until this year because they were so small to begin with and droopy by the time we planted them. Last year the one out front quickly straightened out and last summer started to really grow. This year it has grown some but because we let it fruit for the first time, it hasn't grown as much as I think it could have. They are dwarf apples too.
The leaves do not look burned but are yellow like too much watering is done. I have tested the soil and the PH is 8 and I can't remember the rest.
I have never seen apple trees supported through their lifespan so they must not be gala's. There are a couple of apple groves I see once or twice a year and they are kept very small.

The fully-dwarfing rootstocks have very slow root growth compared to top growth. This is what causes them to limit overall growth. In windy conditions, unless you keep the top small too, most dwarfs will have some amount of rock. The orchards may be using a semi-dwarf or a more vigorous dwarf rootstock that anchors the tree better. The variety (Ie. Gala) only refers to whats grafted on top, not the roots, so there is a lot of different kinds.

I'm guessing that your main problem is minerals in the soil. Where you live is an ancient lake-bed, and has a high concentration of various minerals (sodium, potassium, nitrite, boron). Some of these are toxic in large amounts.This is also contributing to the high PH. Apples prefer acidic soils. Sodium (and other mineral) toxicity often looks like a yellowing leaf with brown at the margin. You can get your soil tested at you state's extension: http://extension.usu.edu/yardandgarden/htm/soils/soil-testing/

Peat moss, pine bark or needle mulch, or sulfur can help lower the PH.

Yea, yea. It has had years of pine needle mulch collecting in that spot and area.
Apples grow very well here with little care. Even in home gardens. Mine seems to be the one that is lacking. It could be that I have an inferior root stock, though I haven't read anything about it doing that.