First things first: There are motors mounts and then there are transmission mounts. Motor mounts keep the engine in place, firmly anchored to the frame. Transmission mounts do the same thing, but for the transmission. 

IF you have loose or damaged transmission mounts, the jostling of the transmission will cause internal damage. From here, it's impossible to say if your mounts are damaged. What is possible to say is that loose mounts can create internal damage in a transmission, so you should not drive the vehicle until the transmission mounts have been repaired, and the transmission is securely on the frame. 

Whether the loss of power when turning is related to the transmission, or some other cause, only a good diagnostician can say. 

There's an old saying in social science: "Correlation does not equal causation." Two things may happen at the same time (like the number 6 and the color green) but they are related in time only. Neither "caused" the other to happen.

You may have multiple reasons why the car loses power, and they may be completely separate from the transmission.

More specifically, there are more than a dozen reasons why you could be losing power while turning: Low compression in one or more cylinders, clogged fuel filter, dirty air filter, dirty MAF, dirty throttle body, congested Exhaust Manifold. ... gummed up fuel injectors, cracked or old spark plugs, etc. . .

Before you spend a dime, you need a GENERAL INSPECTION of the vehicle. Everything needs to be looked at. Don't find someone who just throws parts at problems. 

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Here's a good description of what is covered in a general inspection: http://www.agcoauto.com/content/General_Inspection