I won't comment on the logistical difficulties of making a separate trip to the gym, except to say that there are always a million excuses not to work toward your goals, but if you really want 'em then you'll find another way.

> being so exhausted that the rest of the night is down the drain

This is your body's resistance to a change in routine; you may also observe it when, e.g., quitting coffee or skipping breakfast. Keep it up for a few weeks and you'll be over the hump. A couple more months, and a 30-minute workout won't even faze you.