I appreciate your concerns. You don't have to worry about incompatibility with Tai Chi. There are always lots of posts concerning mixing things, you might want to check out past posts. Just keep them separate, maybe different times during the day, at least 30 minutes apart. I am not familiar with the specifics of Dao-In. The same rule applies, but the greater concern is making real progress in one qigong system, or diluting your practice by duplication and/or wasting energy constantly adjusting to different energy patterns. You have the leeway to try it out, but long term, you should choose, and focus.(regarding qigong exercise) This is the best way to make progress. Perhaps at some point, ask yourself why you practice qigong, and what your goals are. Self healing, healing work, spiritual transformation, teaching, martial arts, etc... Use your purpose here or goals to help discern your choices and commitments. (I might add that your body remembers the systems you learn, even if you leave them for quite awhile.) Unless you are a very high level, I would commit to something specific, long enough to get an idea of what it is. Practicing something to "some extent", might not reveal a higher level experience with the material involved.
