According to the Cambridge definitions, dominate someone / something means to have control over them. Accordingly, I think in my following cases, both sentences in each pair mean the same.
I was wondering if you could confirm my take on it approving this equality:
1) She dominates her children. = She has control over her children.
2) He dominates his emotions. = He has control over his emotions.
3) He dominates the situation. = He has control over the situation.
I think they mean exactly the same thing with a slight nuance which strikes me that the cases with "dominate" are a bit more formal. However, I have no clue about their semantic prosody. Please let me know about it.