Yeah, if Cody understands how to use the door, it's just a matter of time before it occurs to him "huh, I don't have
to ask mom, I can just go out! cool!" Keep doing reminders at routine times (e.g. when you get home from work, etc.). Slowly start to phase those out, make him have to wait longer and longer like housebreaking him. He'll quickly figure out that he's uncomfortable, but he can fix that!
My aunt and uncle have dog doors, and I was living with them when I got Sprocket. He quickly figured it out - I did it as part of housebreaking. He was 12 weeks old when I got him. It took him a week to get comfortable running through the door at top speed with the other dogs. At 13 weeks 2 days, he brought in a 12" plastic flower pot, WITH the dirt still in it!
He was very
proud of himself, even as my aunt and I took it away, he was strutting around all smug - he had to navigate through TWO dog doors to do that. Little did I know that was a predictor of things to come - we hit a point where I ended up closing the door much of the time, because I was tired of taking away giant sticks and pieces of garden hose and other large, random things that he had to work hard to maneuver through the doors).
Sprocket and I have been living in an apartment since November. He hates having to ask to go out. We visit my aunt and uncle's house regularly (couple times a month) and he's always quick to show that there
he can go out without asking, rather than quick potty break on leash and then back inside.
The other two will figure it out as they watch Cody do it. Sometimes they clue in if they're playing "chase" and the lead dog goes through the door - the others follow without realising it, as the flap is already pushed up.