YOU SAID:

There was their house and they are moving in

INTO JAPANESE

彼らの家があり、彼らは

BACK INTO ENGLISH

There are their houses, they

INTO JAPANESE

彼らの家がある、彼らは

BACK INTO ENGLISH

There are their houses, they are

INTO JAPANESE

彼らの家があります。

BACK INTO ENGLISH

I have their house.

INTO JAPANESE

私は彼らの家を持っています。

BACK INTO ENGLISH

I have their house.