Dilemma between present perfect simple and past simple

I do not know where to find the right answer. Please tell and explain what my errors are

I must use either the Present Perfect Simple or Past Simple

 B. How long / you / have /that?
 A. We / have / it since the kids / be / tiny. It / belong / to my parents before us, so it / be / the family holiday home for a long time.
 B. / you / go / there when you / be / a child?
 A. Yes. Then my father / want / to sell it so I / buy / it.

My version

 B: How long have you had that?
 A: We've had it since the kids were tiny. It's belonged to my parents before us, so it has been the family holiday home for a long time.
 B: Did you go there when you were a child?
 A: Yes. Then my father wanted to sell it so I bought it.

I am not sure about the solution in bold. Should it be “it belonged” or “it's belonged”? Is it OK to use the Present Perfect and Past Simple together in the same sentence?

The past simple is the only option for the verb belonged as the action is complete and there is a time reference (before us).

Past simple verbs often have explicit time references to show they are complete

They left the town 10 years ago

I went to the shops yesterday

Past simple verbs also have implicit time references, such as in your example.

At university, he studied chemistry (the tense confers the fact he finished university)

She wrote many great songs in her heyday. (the tense confers the fact that her heyday finished, and she is no longer so great)

belonged (past simple) refers to the specific generation which owned or had the deeds for the house before they were passed on (and hence the action became complete). Hence, previous owners, even if they are still part of your family, and still have rights to its use & enjoyment, etc. are indicated using past simple tense.

As the family home is passed from generation to generation - and used by family members who may not actually own it - it was and still is the family home. Hence, the present perfect has been the family home is the correct choice of tense for the second verb phrase -

So in answer to your question, yes - both tenses are needed for your choice of verbs in the sentence.

I am quoting from a site named "veritasprep.com", which guides students preparing for exams. It gives the following answer to the question "Is it incorrect to use multiple verb tenses in a sentence?" dated August 1, 2017. I give below only a part of the answer.

Tense consistency - We do not switch tenses when there is no time change for the actions.
Example: During the match, my dad stood up and waved at me. The two actions ("stood" and "waved") happen at the same time. So they need to have the same tense.

When dealing with actions that occur at different points in time, we can use multiple tenses in the same sentence.
Example: My dad reached for the sandwich after he had already eaten a whole pizza.

Here the two actions ("reached" and "eaten") happen at different times in the past. So we use both the simple past and past perfect tenses.

Another example: I have heard (present perfect) that Mona left (simple past) Manchester this morning, and has already arrived (present perfect) in London, where she will be (simple future) for the next three weeks.

When using multiple verbs in various tenses in a sentence, we should make sure the verbs convey a logical sequence of events.

The sentence here is “It belonged (simple past) to my parents before us, so it has been (present perfect) the family holiday home for a long time.”

The first clause says: "my parents had it before us" – something that happened in the past – so simple past
"now we have it" - present tense
"so it has been the family holiday home" - an action continuing from the past to the present - so present perfect tense.

The change in tense is consistent with the timing of the actions, and conveys a logical sequence of events.

iiieee.M. Thanks for the question. It has helped me clear some of my doubts.