External obstacles

Training internal and external martial arts at the same time is not so good - the approaches contradict one another.
The external art will impede your tai chi progress.
Tai chi is concerned with whole-body movement, with the emphasis upon the movement itself; the how rather than the result.
Physical movement is largely concealed within the body, and only a small fraction is visible during the application.

External arts are strength-based and focus on speed and aggression.
The limbs move independently of the rest of the body, with a more superficial connection throughout the frame.
Strength is used against strength.