Do you prefer evergreen, like a Holly (such as Oakleaf Holly) or deciduous (like a Bloodgood Japanese Maple)? About how close is 'next' to your house? A lot of trees need to be planted a good deal further away than folks originally plan, so you might want a 'Fireglow' Japanese Maple instead of a Bloodgood, for example. Do you like narrow/columnar trees like a Skyrocket Juniper or Emerald Green Arborvitae, or a somewhat broader-based pyramidal tree (such as Boulevard False Cypress), or do you like the rounded crowns seen with some mature maple trees like sugar maple? By 'ornamental' do you mean flowers in Spring (e.g.: redbud, dogwood), colorful foliage (e.g.: Thundercloud purple plum, I believe, or some Japanese Maples such as Fireglow or Crimson Queen) or perhaps even peeling bark (e.g.: Paperbark Maple)? I know you mentioned 'that flowers,' but be mindful many plants that are highly ornamental when they flower do so briefly, and aren't nearly so impressive most of the year. Richard.

The Cleveland seems to suffer less from the same structural problems as the Bradford, but is as capable of being invasive, so I suggest that you look further for a tree. If you only have 6' of kitty-corner distance, if I am imagining the space correctly, then you really want a narrow tree, that won't get over 12' in width, to fit in the triangular area between the barn and the ramp. Is the ramp in frequent use? If so, then you will need to be careful what you plant so the access to the barn isn't hindered. You can do judicious pruning and limbing up as the tree grows, but still, the less work, the better. What about a single trunk - or only 2-3 trunked - Amelanchier/serviceberry? It throws light shade, and, depending on the cultivar, is more or less native, and tough. Redbud is another possibility, although the shade may be too heavy. Hawthorn, especially one of the natives, might work, although if the ramp is in use, the thorns would be a no-no - I THINK there may be thornless selections. But if fireblight is common in your area, forget it. A selected crabapple might be good - they are pretty tough, and some are less spreading than others. Another possibility might be Chionanthus/fringetree. A taller viburnum, with careful limbing up as it grew, might work. Lilacs, with control of suckers, might also work.

If you've gotten the idea that there are numerous choices, you got the right idea. If you haven't gotten that idea yet, we can bend your monitor for a long while yet. The first things that come to my mind: Apples aren't as disease prone as you might think in the drier summer climes of the upper midwest, and newer apple varieties don't get released unless they have a remarkable degree of resistance. There is a little bit of sliding scale here, but us it as a rule of thumb. If disease resistance is truly a matter of concern, I hesitate to recommend pears (due to fireblight), but they are otherwise free of the foliar problems that bother Malus, but the sweetmeat of the woods is a fall treat not to be missed. I have heard that Parker and Flemish Beauty (my personal fav) are the same thing, but would request confirmation. If redbud really is of interest, do not buy single stem redbud in the Twin Cities, regardless of the strain. Odds are you are going to have a clump sooner rather anyway. And look for the NDSU release, the only Cercis canadensis that survives on the plains of Absaraka (a little NW of Fargo). And finally, when you've made a choice, run with it. Options exist. Many options exist. Establish your criteria, made your decision, and enjoy.

It isn't really necessary to repot and replace soil every two years if the soil mix is properly chosen to begin with. Roof top gardens are a similar situation, and rely on sand as a major component of the soil mix to avoid major drops in planting soil depth. I generally prefer to avoid organic/bark based soil mixes in large planters in favor of using a mix of sand, perlite, and pumice, with 25% maximum coconut coir. This sort of mix, even though it is totally artificial and has little organic/humus content, does not get anaerobic or evaporate over time as a bark based soil mix does. It will require regular fertilizing to maintain plant growth, as there is nothing to hold onto nutrients in such a well aerated planting mix. Repotting can be as simple as removing only the outer 1.5 to 2 inches of soil and applying fresh soil, similar to how bonsai plants are treated, and doesn't necessarily require removing the plant from the container. I'd agree that in general, keeping a small tree in good health in a hot southwest location does require more work than the same plant in the ground, but it isn't difficult if the right plant is selected for the conditions and degree of maintenance to be given. I wouldn't be recommending something like a Japanese Maple for a hot southwest facing wall, as a tree like this can't survive on just twice a week watering in heatwaves, and will most likely get leaf tip burn by mid summer. It would be a much better candidate for an east or north facing wall. Given that the OP wants to only water twice a week, it makes more sense to choose an extra drought tolerant species such as the Olive, or something equally tolerant of heat and drying out. If it is at all possible to provide automatic drip irrigation to these containers, it widens the possible list of potential plants exponentially.