I was in your situation - I was a programmer (now a dev manager) and I put on 20 lbs in 2 years sitting around eating badly. However, I did have the advantage of a life of sports (including nearly 30 years in martial arts now) and a college degree in kinesiology to help me turn that around.
You are already doing TKD twice a week, and jogging in the morning. Assuming that you are jogging at least 3x per week, that should take care of your basic requirements. I would also recommend some explosive type workouts which I will detail. Too much steady state, slower pace cardio can possibly interfere with the explosiveness needed for TKD. While the evidence is not 100%, recent studies in the field have shown that it may be possible to convert from type I (Slow twitch) to type II (fast twitch) fibers in your muscles and vice versa. (There is also some debate about whether it's an actual change or a change in other associated structures, it's all up in the air). But one thing is for certain, past a certain point of basic fitness, you want to train for what you need. If you need quick, explosive movement, train that way.
As far as deficiencies, what I have noted from many years as an instructor and participant, is that the lower back muscles, glutes/hamstrings, rear deltoids and lats are the muscles most likely to suffer. There are very few actual reverse hand techniques (reverse elbow, upset ridge hand, backfist) that use the rear deltoids and lats to any extent, and the front/round kicks get utilized more often than the side/back kicks. Plus, you need basic strength overall.
I would recommend a program such as Stronglifts 5x5, but twice a week rather than 3x, and make sure to add in calf work and back extensions. When you do your abdominal work, make sure to add rotational versions to get the obliques. That should be sufficient to take care of your basic strength needs.
Along with that, you want to train explosiveness and movement, so I would invest in an agility ladder and a set of agility cones. You can find many different drills, but both of these will work your foot movement as well as explosive speed, presuming that you really work it on the cone/running drills. Do this once a week to start, and as you get used to the increased amount of workouts, you can increase it to 2x per week. On your jogs, I would also add in a day where you do strides/fartlek type work, where you put in short segments of uptempo, fast running with short recovery (Something like 10 minutes of 30 seconds accelerate to near sprint, 30 seconds slow jog recovery).
As pointed out, flexibility in any martial art is an enhancement, so I would make sure to do dynamic (sport motion specific) stretching before, and static stretching after. There isn't much evidence that being more flexible helps avoid injury, or that it enhances performance, but a lack of flexibility in martial arts can definitely be a hindrance.
You also should make sure (Especially considering the sedentary nature of your job) that your diet and sleep routines are sound. It's all too easy (as I did) to have soda and sugary/fatty snacks sitting around the desk, but all they will do is derail your hard work. Replace soda with water or unsweetened teas, and the sugary snacks with things like nuts, nut butters, veggies with hummus, and pay attention to total calorie intake.
Give yourself some rest days, and some cheat meals, if you feel like hell, go ahead and take a day off. Mix it up, don't always do the same workouts on the same days, keep it all fresh and fun, and always look for new exercises and activities to support your main emphasis, TKD.