“My yard is fenced with entrance gates at the front and back of the property. I have found during recent weeks that a neighbor has been opening the front gate where the sidewalk is and entering my yard to allow her dog to use lawn and sometimes that side of the house as its personal toilet. Since my yard is gated and the neighbor is entering through a latched gate, can it be considered trespassing? And what legal options to I have to deter this behavior?”
It’s trespassing whether you have a fence or not.
As a practical matter, neighbors rarely end up in lawsuits over canine habits, and there may be some things you can do short of one. Perhaps there is a pooper-scooper law in your area, which your neighbor is violating?