Need too hold a door open, and keep it from closing

We have two dogs, which mostly get along fine. But have fought in the past. My wife just got a new job that is not WFA, so there is not always someone at home with the two of them.

The older dog stays in our bedroom, while the younger one in the living room, with the run of the house.

We also have cats, and they have litter boxes in our bathroom, so i keep the door cracked for them to. come and go. But my son's big orange cat pushes the door open enough the older dog can get out of the room.

Today when I left the house i took a piece of rope, tired it to the doorknob (door swings into the room) on the room side of the door, then using a caribeaner connected the rope to the curtain hold outside our room. This prevented the door from being pushed open any further, however when I got home the dog had pushed the door closed, preventing the cats from getting to their litter boxes.

I am looking for something cheap, or hopefully i can make, that will hold the door in place, open just enough for the cats, but not the dog.

I was looking at something like this, but we have a sweep under the door that would prevent this from working.