This may mean "My father made/let my younger brother learn English". How do I tell which one it means when using the causative?
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Given just the sentence you propose:
You cannot tell whether this is meant to be permissive ("let") or forceful ("make").
What I've found is that when you see the causative (使役), you should assume that it is the forceful version unless context says otherwise.
Also, there's a second way of saying it if they want to say "let":
父は弟に英語を習わせてくれた。 (or 習わせてあげた。/ 習わせてやった。)
In my experience the more positive versions often end in くれた or くださった precisely because this is how they make clear that this is letting someone do what they wanted rather than forcing them to do something.
"父は弟に英語を習わせた" is a causative sentence.
However it depends on the context.
「弟はフランス語か英語を習いたいと言ったが、父は弟に英語を習わせた」The last sentence is causative. Father made the decision which language younger brother should learn.
The clear causative sentence is 「父は弟に英語（学習）を指示した（命じた）」.
Translation: the father had not allowed the younger brother to learn English, but he has finally allowed him to do so.
In this context, the father's intention is not the forceful causative but the permissive causative.
The Japanese sentence 「父は弟に英語を習わせた」can be used for both types of intentions.
If you'd like to avoid using causative sentence, you can just express father's permission or accession:
The sentences above are rather stiff, but if you use the following:
Then it will sound more casual.