Sounds like you are making a commendable effort to care for your physical body! Of course, balance is key. A mistake many of us make starting a new exercize program is expecting too much of ourselves, and then feeling like we are failing. Best is to know how much time and energy you can realistically set aside for self care, and choosing activities that fit your time and convenience (a class or club that requires a long commute can be a real bummer).
That being said, I think Yoga would be a great addition, not only for the stretch component, but also for the self nurturing and stress awareness. You may want to look for a beginner’s yoga class which has a focus on relaxation. Having a well trained instructor who is able to assist students individually would provide the foundation for developing your own yoga practice (which you can do anywhere, anytime!) once you know how to practice safely.
As for resources, I would recommend Mukunda Stiles excellent book called Structural Yoga Therapy. You can use it to tailor a practice for your individual needs, and it provides clear instructions both for assessing structural imbalances and practicing asana. I highly recommend it to both beginners and experienced practitioners.
Namaste,
Chandra