Your mare may simply be letting this filly know who's "in charge" by putting the filly in her place during meal times. My experience is that the older/established horses will back off once a suitable "order" is clear to all individuals.
If you're worried that the filly won't get enough to eat (or your older mare too much), I suggest simply separating them for meal times.
There isn't much you can do about herd politics - other than separating individuals who don't get along. Most of the time squabbles will be short lived, and minor - they are a part of herd life for horses and not usually anything to be overly concerned about.