I have a hard-pressed belief that long commutes are extremely detrimental. Even if you work long hours, if the commute is no more than 15 minutes, it ain't so bad when you get home and you still have plenty of time for everything else. The commute here is the problem, not the work. No shit you're tired. You're working an entire day and traveling 3 hours.

Not saying you should be doing anymore, just saying it's okay to not be productive after traveling that much on top of a full work day. If it makes you feel better I work from home and recently had to travel for a customer. 2 hours each way, and I only worked 7 hours at the customer and it was the most exhausted I had been in months.