So, does it convey different accent/emphasis or something like that?
I'm sorry that I'm asking questions like these, in Russian usually there's emphasys conveyed with the word order, and the word order in the original sentence is kinda baffling for me in terms of conveyed emphasis (whether the stress is on "not hearing", or on "your children"?).
It's probably similar to Russian in this case.
In "Tvoje děti neslyším" the implication might be that you can hear something else, like other children.
Meanwhile "Neslyším tvoje děti" may be something said spontaneously, when you realize you should hear them but don't.
These are just examples, the nuances are quite small.
I don't know much about russian but i guess that the way of emphasizing words by changing word order is very similar or same.
Czech usually emphasises words by putting them at the end of a sentence. (Or sometimes at the first place in a sentence)
Yes, FYI, in Russian, the "news" comes last in the sentence, when other emphasis is not heard or added in writing.
Tvoích dětěj ně slyšu. --I don't hear
Ně slyšu tvoích dětěj. --your kids
What would "I do not hear your children" mean? Where is the difference between can and do in cz?
There is none (I mean, the sentence would be the same). It largely depends on the context (and, to be honest, there are very little situations where that distinction matters, and those are usually resolved with addition of "moci" or some time reference).