FWIW: I am native AmE, and it sounds odd to me... not completely wrong, but a bit odd. Similarly, "Don't talk to me like that" sounds sounds better than "Don't talk like that to me." However, interestingly, "Don't talk like that to me!" sounds less odd than "Don't look like that at me!"
Unfortunately, I can't cite a rule, only make the observation. Perhaps your suggestion could be added as an alternative translation.