No clue what they're called, but the ex's parents had one where you pushed a button and it swung open so you could walk through. The frame was still on the doors, but you didn't have to climb over. They were fabulous.
My sister and BIL got it for their dog but he stopped needing it just before L needed some boundaries. It works great, it is a tension mount, and you do have a locking mechanism to help little hands stay out.
Re: baby gate recs
We have this one https://www.walmart.com/catalog/product.do?product_id=10741056&sourceid=1500000000000003260550&ci_src=14110944&ci_sku=10741056
My sister and BIL got it for their dog but he stopped needing it just before L needed some boundaries. It works great, it is a tension mount, and you do have a locking mechanism to help little hands stay out.