Barb, This can be done with some care and thought. And it doesn't have to be a major undertaking.
It depends on how the jacket is made. If it is unlined, then I think the shortening and hemming would be fairly easy. Just mark how short you want it to be, determine how much needs to come off the bottom, mark carefully, measure again, mark carefully ( yes do it twice) then cut. finish the edge with a serger if you have one, otherwise I would use pinking shears, and do a blind hem or hem by hand. I try to duplicate the amount of hem by what was there before shortening. for example if the hem measures 1 1/2 inches, I would use the same amount. Seems to make the jacket hang better.
Now if the jacket is lined, it is another matter. Is the lining "loose" at the hem or is it part of the hem? Follow the same steps as above but look at how the lining is attached or not at the hem and duplicate it. Remember the lining will need to be a bit shorter than the jacket.
Hope this helps and gives you an idea of what to do.
Murphy

Dear Murphy - thanks so much for answering. I have done a couple of these but where I seem to have trouble is the facing on the front and the hem. Yes, it is lined, but I will try to note what you said. It seems like it was hemmed and then pressed to come down over the hem. Barb

This will be much easier if this is an unstructured, boxy jacket. If it has a waist or is shaped close to the body, you may get it short enough but find it remains too long in the waist. It could look wrong even if you've done a perfect job with the hem.