Poop accidents

Daisy is just 1 year old. She is not 100% trained yet. She poops once in a while on our area rugs, but never on the tile or wood floors. When someone is home, we take her out every 2-3 hours and she is fine. But during the day (on school days) she is alone between 8:30 and 3 PM and we occasionally find poop. We used to be able to confine her in the kitchen, but she has figured out how to squeeze through the dog gate, so while I am trying to get a gate that she can't get through, I am leaving her free in the house. I don't have the heart to crate her for 7 hours 5 days a week.

I give her a treat every time she poops outside, and she seems to get it. How can we "cross the finish line" and get her 100% trained?