After some reading up and research, I came up with this.

Dogs are pack animals as we know but many people don't realise that rank reversal can change depending on what environment we are in. In some places, the dog might regard you as alpha because you just happen to act that way but, somewhere else, you inadvertently give him this role, in your case when you go outside, and then he takes the role of alpha.

The reason I thought this may apply because the following is about a dog that behaves himself perfectly when at the training school but becomes very disobedient again once they leave the training school and, in that way, makes it quite similar to your case.

" Question
I have been attending training classes with my eighteen month old pointer since he was 6 months old. In the class he is the star pupil and he has won a lot of club competitions which are held regularly. However, outside the class he is still extremely disobedient. He pulls on the lead, he won't come back when I call him and he is terrible with visitors to the house - he just won't leave them alone.
He just wants to be friendly, but I know that not everyone likes dogs. If I shut him in another room he barks like mad and scratches the door. Why won't he behave himself outside the class, the way he does inside?

Answer
Teaching the dog what you mean by certain words of command is only part of the training process. As a direct descendant of the wolf, the dog retains a very strong pack instinct and, in a pack, rank has its privileges. If, at home, you are allowing your dog the privileges of high rank, then he will see you as the underdog and someone who has no right to tell him what to do. This is the same in any species that operates in a hierarchical rank structure. Allowing your dog to procede you through doorways and passageways or gateways; allowing him to occupy your bed and chairs but respecting his sleeping area as his alone; feeding him before you eat; allowing him to beg for food from your table - all these are privileges of rank. By inadvertently promoting your dog, you lose the right to lead and control. He may obey you in the dog club, but within that environment he has no other choice. If, however, when the instructor opens the door at the end of the lesson, your dog pulls you out, you have just allowed him to regain the rank that you have tried to take off him in the lesson.
Rank also has responsibilities and among these are that he should lead the pack - that's why he still pulls on the lead, it is his job to be out there in front; to keep the pack together - that's why he will not come back to you when you call, it is not you job; to defend the den - that's why he is so troublesome with your visitors, he is not being friendly, he is making sure that they move around on his terms but in a passive and not an aggressive way. What right do you have to isolate a higher ranking animal, especially when there are intruders in his den?
That's why he complains so much when you try to do so. None of these problems has anything to do with training, they are all to do with attitude. If you get the attitude right and your dog sees you as leader, all your previous training will pay dividends. if you make sure that the privileges of rank are yours, everything else will slot into place."

Hopefully, this will help you understand a little more why your dog acts in a similar way but with the added problem of him being aggressive towards other dogs. If he thinks he is leader, he might think it is his job to protect the pack from intruders which is why he goes mad on seeing other dogs rather than leaving this decision to you. If you punish him, it would make his behaviour worse for the reasons I stated in the above post, and the reason he won't take any notice of you when out is because of what is described above also. A lower ranking individual cannot demand the attention of a higher ranking individual so he ignores you when you do try to demand it. You may need to look at the rank structure within your canine/human pack and demote your dog to help with this behaviour.

Indoors, he may view you as higher but, outdoors, he is probably thinking that the role of alpha is handed over to him.