Overgrooming in cats is not uncommon & seems to be more prevalent in oriental type breeds. There are several medical issues you need to rule out first before you start looking at behaviour problems. Firstly, whilst you've sorted out the ear mites, has she been treated for fleas? If not, this is probably the first thing your vet will suggest. Some cats are allergic to flea saliva which can cause terrible itchiness. Secondly, it could be an allergic reaction to something else, like house mites, dust, food etc. But this can be notoriously difficult to pinpoint & may involve lots of skin tests & other expensive veterinary treatments.
Having said that, as the overgrooming is confined to her lower back & abdomen, it seems quite probable that this could be a stress-related issue. The grooming is almost like a stress-reliever & once they start to make themselves feel better by grooming, they can be quite obsessive over it, to the extent that they lick the fur away & can start to make the skin sore & raw. This leads to more itchiness, so more grooming & you're in a vicious cycle.
You say that your new cat doesn't like your other cat & whilst there might not be any out & out aggresssion & fighting between them, there could well be quite subtle body language signals going on that you need to be quite observant to spot & would be a signal that all is not well between the cats . This alone can be a cause for stress in your cat causing her to overgroom.
I would suggest that your first port of call should be your vet so that any medical causes could be ruled out. Possibly a course of steroids to relieve any itchiness & inflammation? If there no apparent medical causes then perhaps ask your vet for a referral to a qualified feline behaviourist to help sort any factors in your cat's life that are causing her stress & anxiety.
In the meantime, you could try the following:
Make sure that both cats have separate areas that they can go to for resting/sleeping, lots of warm beds, at different heights around the house. Put out lots of e.g old towels, jumpers, fleeces, vetbed etc, in warm draft-free places in different rooms.
Do the cats use a litter tray? If so, make sure you have at least two in different locations (& possibly a 3rd if you have room ~ you can always remove any that they don't use).
Have separate feeding stations & several water containers around the house.
If one cat is particularly wedded to one room in your house, try to make that room as comfy as possible for that cat & if possible, try to make another room as a sort of "comfort zone" for the other cat so they each have a room to call their own.
Scratching posts, toys, if they use them, can be placed in their rooms as well. If they both enjoy your company, try to spend quality separate time with each cat.
It may be that things will settle down as they start to realise that they have everything they need without having to worry about the other cat, but if not, you should really consult a qualified behaviourist who can visit your house & help you sort things out. I wouldn't just leave it to carry on as the overgrooming can get quite serious & the longer it goes on, the harder it is to sort out.
Best of luck ~ I hope things get better for your cats.