For you'r practice it may be the correct way.
What you’ve shown of Chang Taiji training violates many of the principles we use and follow.
A few thoughts.
Tai Chi is not neijia in the sense that neijia is not Tai Chi. An easily understandable point. But what causes great difficulty for most is that in the same way as Tai Chi is not Neijia,
Tai Chi is not the idea that the yi leads the body through the force of qi because yi leads qi and qi leads the body. It's not the training method, which is that the body leads qi.
Tai Chi is not either the idea of sensitivity -- Ting Jin, nor the idea of sticking to your opponent. Tai Chi is not the result of years of hard work and practice.
Tai Chi is not the ideas of Traditional Chinese Medicine in any of it's streams -- such as Daoist Qigong -- or whatever -- mixed with "Shaolin Martial Arts"
whatever that means.
Tai Chi is not your personal pet project. You don't get to learn Tai Chi. You get to learn from a master and follow the master. You are learning what they know, not an abstract concept that you can own. Tai Chi is not something you can experiment with, add BJJ to, or make up.
Tai Chi is also not Wu De, the study of the Confucian Philosophy of the Taiji tu (hint: Tai Chi isn't daoist).
And yet paradoxically, Tai Chi is all these things.
Johnwang once wrote that to be captured by style is a mistake, and one must break free of the restraints of style. Many other people have commented that one should work with natural instincts and impulses. I'll even drop a name -- Joanna Zorya, whose "Martial Tai Chi" was an interesting attempt to "ditch" the "mysticism" of Tai Chi (ex. Chi) and get back to the martial roots. What few realize is that she just took a few wing chun and judo classes and attempted to teach those as if they were Tai Chi. That's exactly what Mr. Moy Lin-Shin did with his Liuhebafa-- he took a few Tai Chi lessons from Raymond Chung (3-6 months) and then created Taoist Tai Chi.
But the real issue here is that yes, Tai Chi is individually none of the above but paradoxically all of them, because this is kind of like a basic foundation. However, there is one thing you must have or you are not doing Tai Chi -- because, individually, all of these are actually requirements for other martial arts. Wing Chun, Xingyi, etc. all speak of these kinds of things.
But what makes Tai Chi special is the concept of peng, lu, ji, an. Without the foundation above, you can't have Tai Chi. But it's what you do with the foundation that makes it Tai Chi. Breath? Meaningless. Can we be honest and trust each other for once? Every Chinese Martial Art, every qigong, daoi, etc. all has breathwork practice. Let's be real. If you are haggling over breathwork you are worried about beginner level things. Meaning, if you can't understand breathwork easily -- forget Tai Chi, you wouldn't be able to do any kind of physical practice! In the end, breathing is just not that difficult (or, important).
There are so many more important things to focus on than the breath when trying to determine what is correct in Tai Chi. For example, standing. Every Chinese martial art has standing. Tongbei, Chaquan, Baji, Eagle Claw, you name it. It's not standing. It's Peng, lu, etc.
What this means is that if you want to call what you are doing Tai Chi, you must use Peng, Lu, Ji, An. If you cannot clearly identify Peng, Lu, Ji, An, in form and push hands, then you are categorically not doing Tai Chi. You may be
learning the Tai Chi form, going in the right direction, but I think too many people take that as mastery these days.