I know from posting for years, that you have a fairly demanding and time consuming job. Unfortunately, so do I...lol! I am a regular exerciser and my husband introduced me (back when we were dating) to a book "Body For Life" which subscribes to 30-45 minutes workouts alternating cardio and strength. I still follow a rough version of that. It is about intensity, it doesn't have to take hours in the gym to make an impact.
It is almost important to figure out when you are in the best mental state to exercise. I get up at 4:15 am on weekdays, so I can have a cup of coffee, read a bit on the internet, get in our home qym (well equipped) get dressed and by at my desk by about 7:00 or 7:15am. It is brutal at times, but makes me feel good mentally and physically. I workout 5-6 days a week. My rest day is always on a weekday, for the record. For me, I could never do it after work. I do not get home early enough to exercise before dinner and I cannot have a strong workout on a full stomach.
This is not meaning to be a lecture at all, but rather to give some gentle encouragement. It is about trying to start small and see where you can fit it in.