I exercised my pup early on, both on and off, but lots of it off-leash. I watched him for signs of fatigue, and he seemed fine. However....I just finished reading "Calming Signals" by Turid Rugaas and also many of the questions and answers on her website. If I could go back, I would definitely do LESS on-leash walking. Two miles is a lot at that age I personally think. Possibly too much IMHO, and I'm only saying that because I just went through it and wished I had gone a bit slower.
Sometimes they're like a child and can keep going long after they should quit. The thing is, it can overstimulate them and cause them to get a bit stressed out, therefore they might act up at home and in the house and then we think they're not tired enough, so it can be a bit of a vicious cycle. Also, it's easy to expect a lot out of them too early in terms of on leash behavior. I always stopped when my pup was pulling, so sometimes (we didn't do two miles at that
age of leashed walks for sure but at 5-6 months we did) it would take a long time (plus a mile of ours is uphill at about 8% grade), meaning he was out there "learning" for a long time. I don't correct or anything yet, but still--that's a lot for a pup. I've cut that back, at the age of 7 months and he is calmer and happier. We still do the off-leash hikes, because he LOVES that, but that's different.
Just my .02, but being reluctant to go
and happy to come home
might signal he doesn't love it that much either and it's overstimulating to him. When we do the off-leash (I live in the mountains so there's a trailhead across the street about 50 down the gravel road) he can barely contain himself and when we get there on the way home, and he sees the gravel road, he slows w-a-y down....I practically have to pull him home, LOL. That to me tells me he likes being out there.