Hi A.,
First, Yes you do need to take in to consideration what your reaction is when there is an infraction and whether or not your boxer has a routine.
I am assuming, since you keep him outside that you have a backyard that your dogs can go to at will? If so, this is good.
I have 4 dogs, all pretty big. A Rhodesian, a Pit, an Amstaff and a Lab. I tell you this because your boxer is in no way stupid. He is a large breed and p'oed over something. All sz breeds can and will get pissy over things but it is very important to not let a large breed believe he can dictate anything to you.
This is how I trained all of my dogs, First, get a spray bottle, and fill it with cold water (this is to be used if all else fails).
Find your "sound". Mine is "Beh!"
Make your dog sit for EVERYTHING and do not let that butt get up from that floor until YOU say so, make him sit and stare at his food bowl until you tell him he can eat.
If he wants in/out never let him go in/out ahead of you.
When you see him with a dirty diaper, tell him (in a calm,stern voice) NO, DROP IT. if he just looks at you, or walks away, go to him,(take your water bottle). say it again and add your sound. Still not listening? Then its "I said NO, DROP IT" and squirt him (straight stream on the body, NEVER in the face). As for the potty issue, if you do not have a crate PLEASE invest in one (you can get one pretty cheap on Craigslist)a dog will not usually soil in his/her domain. So, if you cannot watch your dog, crate him. And every couple of hours let him out to potty and drink.until he is trained. But as I said, do this when you cannot watch him, he cannot LIVE in a crate. All of this will take time, as I said, your dog is not dumb but initially it will be a power struggle. But, if you get serious about incorporating training methods, one day it will seem like a miracle occurred, he will just GET IT. Through ALL of this, you need to show this dog lots of love and confirmation for the good behavior, all training needs to be tempered with love.
Oh! And a very helpful hint that I got from Ceasar Milan was that because Dogs truly are Pack animals, you need to be the pack leader, use all the ways mentioned above and add to it using your hand as a pseudo "mouth". If for instance, you want your dog to leave something alone and walk away but he will not, make your hand like a claw (remember when you were a kid?) and use the tips of your fingers on the side of his body (between the neck and shoulder) and "bite" him with a jab motion using just enough pressure for his sz body. The dogs initial response to this should be backing up a bit with a look on his face like "HUH, I didn't know you were a dog!" but may or may not leave the area. Do it until he does.
Good luck! And will you please let me know if I helped you? THANKS
B.