We weren't that surprised that the lab sussed both pushing the door to get out and pulling to get back in but the setter did surprise us since she was so much slighter than the lab (and they really are stoopid!) Maisie (current cat) has a flap and is perfectly capable of using it but if we're in the conservatory (90% of our home, waking time), she'll usually try looking pathetic and when that fails to get the door open, she'll start pulling the inner flap to annoy us until we weaken. Works every time! Her other trick is used after we lock the flap to keep her in at night (mainly for our peace of mind but also to reduce her predation...) She'll go into her litter tray and scrub around as if she's about to "leave a deposit" then her little face appears around the edge in hope that she'll be allowed out for the ablutions/constitutionals. When we have been taken in by this ruse, she just went out and sat on the shelves under the window sills (originally placed there for plant troughs) watching whatever cats watch as they stare into the dark so no we simply ignore her ploy. 90% of the time, the litter tray threat is a bluff so we reckon we're the winners!
Back on topic! I'm sure I've seen motorised cat flaps, including ones for large cats which I reckon would be big enough for small dogs such as bichons. Can't remember where I've seen them though - if I spot them again, I'll make a note of the make and model.