預ける and 預かる: the entrusting party and the keeper
Read who entrusts something and who keeps it. Distinguish the recipient marked by に from the source marked by から in the selected examples.
The party entrusting something
預ける, read あずける, means entrust or deposit. 旅行中は猫を姉の家に預けることにした。 says that someone decided to leave the cat at the older sister's house during the trip.
猫を is the object and 姉の家に the intended place. ことにした reports a decision, not confirmation that the other party has already taken the cat.
The party looking after it
預かる, read あずかる, means keep or look after. 旅行中の友人から猫を三日間預かった。 says that someone looked after the traveling friend's cat for three days.
The subject is the keeper, and 友人から identifies the source. Keep the entrusting and receiving actors aligned with the verbs.
The recipient and the source
使う予定のないお金を銀行に預けた。 says that money not planned for use was deposited at the bank. 銀行に identifies the recipient side.
姉の家に and 銀行に give the destination of entrusting, while 友人から gives the source here. Whether an item is borrowed for use is a separate purpose question.
In 友人から猫を預かった。, does the subject or 友人 keep the cat?
Show the answer and why
The subject keeps it. 友人から gives the source from whom the cat was entrusted.