There are some simple rules which can help you to make good defining adjective clauses and avoid mistakes.
Right: I like people who are on time.
Wrong: I like people, who are on time.
A relative pronoun is a word which signals the beginning of an adjective clause. If the adjective clause describes a person, we can use 'who' or 'that'.
The family who live next door to us bought a new car.
The family that live next door to us bought a new car.
If the adjective clause describes a thing, we can use 'which' or 'that'.
If the adjective clause shows some kind of possession or who something belongs to, then we use 'whose'.
Please notice we can use 'whose' for people or things.
We can use the relative pronoun 'where' for places sometimes.
Finally, the tricky rule. We can omit the relative pronoun if it isn't the subject of the clause it's in. However, if the relative pronoun is the subject of the clause it's in, then we have to use it — we can't throw it away. For example:
In the first example, please notice the defining adjective clause is 'that she gave me'. In the second example, notice how it's possible to drop the relative pronoun because it's not the subject of the verb in the clause. (The subject of the verb in the clause is 'she'.) Both examples are good English — you can use either one.
Okay, a new example.
Right: The police arrested the guy who hit my car.
Wrong: The police arrested the guy hit my car.
The second example is bad English because “who” is the subject of “hit”. The verb in the adjective clause needs a subject, and that subject is the relative pronoun “who”, so we can't omit it.