I am confused because I prefer Program 2, but I do not want to miss out on the benefits of full body workouts (in terms of Testosterone and GH production). Also, I train Muay Thai 3-4 times a week. Thanks in advance."
This is a great question and tough one at the same time. First off, I would have to ask, why do you want to add mini-workouts? Are you under trained or overweight? What is your goal?
Mini-workouts are designed to help people sneak in extra workouts who need it. Think of the busy soccer mom or weekend warrior who has a job and responsibilities. If you actually have time for 3-5 weight training sessions and 3-4 Muay Thai sessions per week then I would question whether you need mini-workouts? John Berardi's G-Flux program dictates that you need at least five hours of solid training each week to push your metabolism to optimum levels. With your regime the exercise volume is closer to 9 hours per week!
To be honest the best type of mini-workout for you would be a nice walk or bike ride twice a week as active recovery. Or maybe a good long stretching and foam roller session to really work the kinks out. You should not need additional intense work. If you have a glaring weakness such as hamstrings or back (almost all North Americans have a weak posterior chain) then address it in your strength training. "Train what is weak and stretch what is tight!" (Dan John). If the purpose of the mini-workout is to burn fat, then make sure it is nothing too stressful as your volume is really high and could have the reverse effect. Think of a quick little body weight routine to get your sweating and panting, nothing too crazy though.
To really answer your question, full body split three days a week or Dan John's One Lift A Day, I would ask yourself what you can follow the easiest given your time commitments.
Dan John's One Lift A Day program is excellent and I used it myself as a stand alone and while training in Muay Thai. The OLAD will make you bigger and stronger but it will also take a lot a lot out of you and requires time to train almost daily. Ask yourself if you can do a really tough strength training session 5-6 days per week on a regular basis?
I would not suggest doing much if any mini-workouts if you are combining OLAD with Muay Thai during the week. You are already getting enough volume and metabolic stimulus to have a very fast metabolism and build muscle. The biggest challenge here will be eating enough protein and nutrition overall and getting enough sleep to recover from all this work! Don't forget, OLAD is 45 minutes of a compound movement. Not 30 or 35 minutes but 45 minutes of squats, or deadlifts, farmers walks, etc. It will send your metabolism through the roof as long as the reps are above 2 per set! If you choose to go with OLAD make sure to take some workouts outside. Do a lot of carrying and throwing workouts especially this time of year. Have fun with it and get creative!
A full body three times per week routine will give your body more time to recover and so will permit the use of more mini-workouts. But is that really your goal? Again, keep them pretty easy as the strength training with the Muay Thai will be plenty of work. I would recommend this program more in the winter months when you can't train outside. Try to keep the workouts under 1.5 hours because of all the other work you are doing.
If I had to choose one program right now I would go with Dan John's one lift a day because it is summer so you can add all kinds of variety like dragging, pulling, carrying and throwing movements for strength. Overall I think the take home message here is to realize that you only need to do so much training each week and need to give the body ample time to recuperate and adapt. Get lots of sleep, eat lots of protein and if you need to sneak in a mini-workout because you missed a session or will be busy that night, go for it! But, if you are training as much as you plan to, they might not bee needed.
Below is a great video of a guy taking his hardcore training outside. This is a great idea for any athlete!