What type of complete feed are you using?
It could be the other horse that's not digesting its food properly and Annie is picking it out. If you're feeding one that has actual grains in it some might be passing through undigested - happens with oats and corn in particular.
It does sound as if she is missing something in her diet.
Have you tried hanging mineral blocks around the place?
Re the garlic - Its commonly fed seasonally in the UK as the smell seems to help deter the biting 'midges' we get there and I've never had a horse suffer with any problem from it, most research seems to indicate that the risks occur if you feed over and above the recommended dose and where you source the garlic from.
Whether or not its worth feeding to a horse as a general supplement if its already on a complete feed with added balanced minerals and vitamins would be very unlikely Equine Health Education