Looking for a Dog Gate like the old screen doors. No latch on one side, but have to pull open to use for dogs, and with a Stairlift.

I have a weird situation. We have a stairlift for my daughter. So we have a piece of cardboard blocking the stairs. But after getting her into her wheelchair we always forget to close off the stairs.

I HAVE to have someway to keep the dogs from going upstairs and rummaging through her stash of snacks. We've had many thoughts, but it always come back to, she has no fine motor coordination, so she can NOT mess with a latch, at all. Was thinking about the old fashioned type screen doors that would slam. (Miss that sound at Gramma's!!) But going up might get a problem. Any ideas or suggestions GREATLY appreciated.