I want to echo Aeon Akechi's comment that your example usage of "heart is in the right place" seems a little strange to me. I've seen it most commonly used in cases where the action produces a result out of line with the good intentions; maybe somebody beats up their sister's boyfriend because they think he treats her poorly. That obviously doesn't improve the situation, but perhaps their heart was in the right place. Staying out late and drinking is (presumably?) bad for children.
That said, I think I can help with your question. In English, I see two main usages for the phrase
one's heart being in the right place. The first is the one you describe
This phrase is used in situations where you mean well but your actions come across harsh or misguided.
Although I primarily see this in past tense, for something like
he did X, but his heart was in the right place. The closest thing I can think of in Japanese is 良かれと思う (more commonly as
良かれと思って). See also here and here. This is typically translated as doing something
with good intentions or
meaning well, but that's what
heart in the right place means when applied to a specific action.
The other usage is to describe people in the general sense, referring to a pattern of poor action despite good intentions (somebody to whom the above case applies regularly). This is the translation you mostly find in dictionaries, like here and here. Something like
心が優しい is more a statement about the person than their motivations at any specific time, but so is
his heart is in the right place in
My friend often gets in fights, but his heart is in the right place.
I can think of no perfectly corresponding idiomatic phrase that covers all uses of English's usages for
one's heart being in the right place.