The phrasal verb take in has 10 definitions in Collins.
If you take someone in, you allow them to stay in your house or your country, especially when they do not have anywhere to stay or are in trouble.
The monastery has taken in 26 refugees. [VERB PARTICLE noun]
- PHRASAL VERB
If you are taken in by someone or something, you are deceived by them, so that you get a false impression of them.
I married in my late teens and was taken in by his charm–which soon vanished. [be VERB-ed PARTICLE]
1.I was taken in by this kind man into his home.
2.The man was taken in into a cave by the storm.
Your example 1 is grammatical. As for determining the definition of this phrasal verb, context plays an important role. In your example, the context is clear enough.
Example 2 does not seem natural.