It isn't a dominance thing. Basically, he's a toddler who doesn't want to get up. A kid would whine or cry or maybe slap at your hands but a dog will growl (whine/complain) and if you don't listen to his complaint he will bite (the kid slapping or hitting out).
Read the sticky on "The Bite Stops Here"
First, you need to train a command for him to exit the crate. You shouldn't have to reach in for him and bodily move him at all. You can try "Out" or "Move" or whatever simple command. Start during the day when you have an hour or two free. Ask him to go in the crate, lure with a treat if need be but don't physically move him. Then feed treats (small ones, you're going to be feeding a lot of treats; if he is food motivated, just use his kibble) through the crate at the top-back of the crate. Only give him a treat if he is calm and has all his feet on the ground (not pawing the crate sides). This is setting up that the crate is a good place. Then open the crate door with one hand and treat him (at the back of the crate) with the other hand. Shut the door. Open the door, treat, shut the door. Repeat for about 15-20 minutes.
Then, put a leash on him. Don't let him out of the crate yet. Continue to open the door, treat at the back of the crate and shut the door. 10-15 minutes.
Now, open the door and ask him to exit the crate with your command word. You can hold a treat out for him. When he steps out on command, give a treat. If you have to tug the leash to get him out, don't treat but don't make a big deal about it, just ask him to go back in. Ask him to go back in and give a treat if he steps back in on command. Shut the door, wait a minute, open it and ask him to exit the crate. Treat if he steps out on command. In and out. In and out. Treats for obeying the command, no treats if you have to tug the leash. Don't repeat a command that isn't obeyed, you don't want to teach him to ignore a command.
In addition to 2 long walks a day, he should be getting several short training sessions daily. Try 5-10 minutes at a time of puppy push-ups (sit/down/sit/down/sit down), 5-10 minutes later of another command.
I prefer my dog(s) to wait while I open the door and then step through the door first so I can pull the door shut behind be and lock it. If we are exiting the house, they go out, I pull the door shut and they stand and wait while I lock it. Reduces me tripping over them and reduces the storm door from slamming shut on their legs/tails if they were to try to come inside behind me (hard to hold the door open if you've stepped through it ahead of them)
Read the sticky on "The Bite Stops Here"
First, you need to train a command for him to exit the crate. You shouldn't have to reach in for him and bodily move him at all. You can try "Out" or "Move" or whatever simple command. Start during the day when you have an hour or two free. Ask him to go in the crate, lure with a treat if need be but don't physically move him. Then feed treats (small ones, you're going to be feeding a lot of treats; if he is food motivated, just use his kibble) through the crate at the top-back of the crate. Only give him a treat if he is calm and has all his feet on the ground (not pawing the crate sides). This is setting up that the crate is a good place. Then open the crate door with one hand and treat him (at the back of the crate) with the other hand. Shut the door. Open the door, treat, shut the door. Repeat for about 15-20 minutes.
Then, put a leash on him. Don't let him out of the crate yet. Continue to open the door, treat at the back of the crate and shut the door. 10-15 minutes.
Now, open the door and ask him to exit the crate with your command word. You can hold a treat out for him. When he steps out on command, give a treat. If you have to tug the leash to get him out, don't treat but don't make a big deal about it, just ask him to go back in. Ask him to go back in and give a treat if he steps back in on command. Shut the door, wait a minute, open it and ask him to exit the crate. Treat if he steps out on command. In and out. In and out. Treats for obeying the command, no treats if you have to tug the leash. Don't repeat a command that isn't obeyed, you don't want to teach him to ignore a command.
Removing from a room works very well with consistency. The dog wants attention, "telling him off" is a form of attention. Like the child that acts up in class so the teacher will pay attention to him. Quietly and calmly remove him from the room for a minute or two each time he gets nippy, then bring him back out to play again. You might have to do this 20 times in a row at first, but he will catch on that he can either play nicely or be bored.
He wants attention. Being told off is attention. If he has had enough exercise that day (and being in a crate at work isn't exercise, although it is helpful for potty training to be around someone), then you can ask him to go to his crate and give him a Kong or nylabone to play with. If he hasn't had enough exercise, then you need to give him some exercise and a short training session (mental work is tiring)
In addition to 2 long walks a day, he should be getting several short training sessions daily. Try 5-10 minutes at a time of puppy push-ups (sit/down/sit/down/sit down), 5-10 minutes later of another command.
If you want to go through doorways first, then you can train him to let you go through doorways first. But if you want him to walk through first, train for that. It is 100% personal preference and the dog will not in any way see who goes through a door first as some sign of his "place"
I prefer my dog(s) to wait while I open the door and then step through the door first so I can pull the door shut behind be and lock it. If we are exiting the house, they go out, I pull the door shut and they stand and wait while I lock it. Reduces me tripping over them and reduces the storm door from slamming shut on their legs/tails if they were to try to come inside behind me (hard to hold the door open if you've stepped through it ahead of them)