I use Witch Hazel, that you buy off the WalMart shelf, at my vet's recommendation. I put some on a paper towel but make sure NOT to soak the paper towel.
As far as cleaning ears that don't want to be cleaned, it's something you have to work up to gradually and earn the horse's trust. Not wanting the insides of their ears touch is perfectly understandable, but there may be a time when the vet has to look in there. If the horse won't let it's ear be handled, then the vet will twitch your horse and I am really really opposed to twitching.
One thing I learned when sticking a damp paper towel, or baby wipe, in the ears is to not make eye contact with the fussy horse. I started out having to look at the floor because I have vertigo and can't look up too high. Naturally the fussy guy is my tallest at 16.1H and I am only 5.2, and I don't have time to be dragging a stool around when there's four horses to get ready for turnout
It takes fussing with them every day - especially your mare. At some point somebody has most likely grabbed her by her ear(s) to hold her in place to do something. It is no surprise to me that the ear my horses least like fussed with is the left one - old memories are hard to shake
Tractor Supply sells soft bristle brushes that are only about 3 or 4 inches long?? Little tiny things that do a bang-up job of massaging that ear hair and just about putting the horse to sleep
They're not expensive and would be a great way to get your mare used to having the insides of her ears handled
Hope this helps
EDITED TO ADD: I almost forgot - my Arab gets that black gunk in his left ear; once he realized I was helping him by removing that stuff, he now puts his head into my chest and will twist his head around, trying to help me get that stuff out. I know when he needs his ear cleaned because he will start rubbing that side of his head against the stall wall.