Translation:Generally I only sing for my daughter.
That's a really good question. It's quite a different meaning. In the accepted answer, I sing for my daughter and no one else does. In your version I am the only one who sings for my daughter. So how do you distinguish the two in Spanish?
I think the answer is that you need to emphasise the "I", which would be done as "Generalmente solo yo canto para mi hija".
I think you've misstated this - the two interpretations you've given are synonymous.
I agree with your interpretation of jasaucedo's example, and both of your interpretations apply to it.
For the original Spanish sentence and English translation, I would interpret this as meaning that (generally speaking) I sing for my daughter and I don't sing for anyone else.
Since English depends heavily on word order to convey meaning, a good writer would place the word "only" very carefully to convey the correct meaning. The rule is to place the adjective or adverb as close as possible to the word that it references. However, in normal conversation, many people don't even think about the placement and listeners ascertain the intended meaning based on context.
Only I sing for my daughter. (Only I, and no one else, sings for her.)
I only sing for my daughter. (I don't read poetry or play the piano or entertain her in any other way. I only sing.)
I sing only for my daughter or I sing for my daughter only. (I don't sing for my husband or for my son or for anyone else.)
Like jasaucedo, I am curious how each of these meanings would be conveyed in Spanish.
"Usually" is "usualmente", The difference is subtle in both languages. "Usually" refers to how often things happen, and is quite neutral, whereas "generally" doesn't relate to how often things happen. For me, in this sentence, "generally" refers to a personal choice. I.e. I choose to only sing for my daughter.