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"Strong enough" begs the question of how much strength is actually needed. Is your reverse trike going to be significantly lighter than the four-wheeler you are using the parts from? Presumably it is, but you would need to make certain.
If the rear wheel carries the same load as one of the two rear wheels of the four-wheel setup, then the stock parts (hub, bearing, etc.) should be quite strong enough. The swing-arm needs to be strong; the design you show could provide enough strength, but you will have to make it out of the right materials and brace it properly and so on. Lots of details that will make or break it.
For brakes, you will need to re-engineer the system to at least some extent. The car parts will be set up to push enough volume for two front brakes and two rear brakes. There will be two brake circuits, either one feeding the front and one the rear, or with each feeding a diagonal (LF/RR versus RF/LR). When there is only one rear brake, the volume that one circuit has to move will be significantly different. You also have to consider proportioning; if you have too much rear brake bias the rear will lock up first, which will tend to make the rear of the vehicle try to become the front of the vehicle.
So you will have to address the brake system pretty carefully and work through the volumes and pressures with some care.
Even if you put both rear brake calipers on the single wheel, you should get a lot more clamping force for a given pedal pressure on that one wheel than on two wheels. So you would want some sort of additional proportioning mechanism...
I know that there are racing parts that can be used to limit the brake line pressures going to at least one circuit; possibly there are ones that can work on two circuits (for the diagonally-linked brakes).
Unfortunately, it is not as simple as it looks at first. Plan on a good bit of testing...
-soD
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