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Try doing a search and you will see an incredible amount of information about balancing bike training with strength training. You will even find information in the Trainer Road blog.
I do low volume plans alongside my daily commute and handle that fine. However, how you will handle it, as well as doing your strength training, is highly individual.
TR also offers outside variants of all of it’s workouts so you might consider trying to encorporate this in to your commutes.
Here’s some reading: