It sounds like you have a good foundation to his training, but because he is so easily set off by other dogs you have more work to do, and because he is so bright you have to work even harder. Bright dogs can be a challenge because they are so highly aware of all of the subtleties in their world and are able to respond so quickly it seems he reacts without giving any warning at all.
The way we look at this is on a few levels.
First - the more you engage his mind throughout the day the better. It's like having a mischievous child in the house, you have to watch them and let them know you have an opinion about what they do. This causes them to become more thoughtful and less reactive. Every behavior he exhibits that you don't like comes from the reactive/impulsive/impatient/independent side of his brain. But when you start to engage his mind more then he begins to think and check in with you before he reacts. If your dog checks in with you first and you are ready with an answer then most of your problems will disappear. There is also a change in his brain chemistry. When he is in the reactive side of his brain there is a release of adrenaline which gets him more excited, but when he is in the thinking side of his brain he has a release of calming chemicals like Serotonin which calm him. So the more you engage his mind and he works with you out of relationship (not bribery or force) the calmer and less reactive dog he becomes.
Second - at the age of 2 he is striving to establish his place in the world. He is thinking that he is an adult and perhaps he can be in charge. Just like a teenager who thinks they know it all and don't need to listen to their parents anymore. Anything that is missing in his training or relationship with you gets magnified right now. You need to meet his challenges or this behavior will become his habit.
Third - you need to practice his skills at the four levels mentioned earlier. But know that there are levels within levels. You can have distances in the house. You can have distractions in the house. You can have distances and distractions at the same time. Like taking a child from elementary school to college there are grades within the levels of elementary, middle school, high school and college. But if you take a fourth grader and send her to college she will fail and it's not her fault. We asked too much of her and she wasn't ready for it. So perhaps having your dog around other dogs at this point in time is asking too much of him for his lack of impulse control. With proper training he can get there quickly (minutes not days) but he needs you to help him develop impulse control.
Impulse control means that you ask him to do something like a sit/stay and then toss something near him and he doesn't go for it. You begin with low level distractions and raise the bar to higher and higher levels and eventually be able to have dogs walk near him and not have him react. You should achieve success in minutes not days.
You will start to notice the subtle signals he gives when he is listening to you, when he is checking in with you and when he has accepted what you are asking. You will also notice the things he does when he is thinking about ignoring you. For instance when he is about to break a sit/stay he will lower his head a fraction - that is your opportunity to remind him what you are asking him. When he raises his head then he is accepting what you have asked for. When he sighs, he accepting what you are asking. If he lays down he is accepting it at a deeper level. When he kicks his hips off to one side he is accepting it at an even deeper level.
Before you get eye contact you will probably get an ear twitch. Ears are like radar, and you will start to notice that he will twitch an ear in your direction as if to ask "do you have an opinion about what I do next? Any advice?" If you don't answer that question he will think "well, you don't seem to care or have an opinion, so I will do what I want to". This can all happen in a flash, so you have to heighten your level of awareness and the timing of your reactions.
Because he is so bright you will benefit from expanding his vocabulary everyday. The more you work his mind the deeper your connection will become, the better he will be at listening and the faster he will respond to your requests.
There are also the obvious discussions on socialization and good manners in general. But to start he has to be able to control his mind and body from making the wrong choices and listening to you better than he does now.
This is not about finding better treats to distract him from other dogs, this is about YOU being an even better treat (your kind touch, your warm tone, your happy energy) because you are more interesting than other dogs.
Its also about practicing A LOT!!!! You don't get good at anything without practice. You don't show up for a competition and expect to win unless you have practiced a lot. It's not 'practice makes perfect'. It's PERFECT practice makes perfect. So you have work to do.
Please feel free to call if you need ideas and help.
Love Them & Lead Them,
~Elizabeth & Doug
Dog Training the Way Nature Intended