don't worry about your cadence it will improve with time. As you did while following the father/son pick up your pace for awhile try to keep at it for awhile. While commuting look for telephone poles, speed limit signs or whatever and push yourself to those spots. It may not be a good idea on the way to work but on the way home push yourself once a week. See if you can beat your previous best time. If you have hills try standing and pedaling up one day another day try spinning the pedals fast and see how that feels. For riding less than 2 months and doing 45 miles you are doing great.

I think the important part is not just to ride slow all the time but push yourself once in awhile depending on your age, weight, sports background this could vary a bit. But, one day you will suddenly notice you dropped your commute time and you felt like you were in your slow mode. I found after taking a break during the winter the next spring I was actually faster than the previous fall.