- Daisy was teaching Taekwondo to a group of children.
- Daisy was teaching a group of children Taekwondo.
Which is the correct usage of "teach"?
The first is more explicit. The second is acceptable, but this usage can be harder to parse, especially in more complicated sentences. For instance, "Daisy was teaching New York Chinese Americans British English" is much more confusing than "Daisy was teach British English to Chinese-American students from New York".
Both forms are acceptable. It's worth knowing that second sentence construction is one with indirect objects, which represent the recipient of the direct object. In fact, alternative phrasings that avoid indirect objects almost always use "to" or "for" like in your first sentence.
There isn't any real difference between the meaning of the two sentences. There might be a small difference in emphasis due to word order (did we first think about what was taught or who we're teaching?), but that's trivial.