My family is pretty tight (and we do happen to be from the Western hemisphere).
One of us was diagnosed with cancer, so the rest of us came together and each took our turns being chemo-buddies (you just go with them, and be there for moral support).
Because they're family.
We are family, is an expression in English (and a really good song) that means we will provide assistance, because it's an intrinsic responsibility and, according to my mom, "your DUTY as a member of this family."
'Family' are the ones who will always be there for you, no matter what (regardless of blood relation).
IMO, you might need to find the word that means not this, as (at least in mine) family already implies it. That's why we have words like estranged : (no longer close or affectionate to someone; alienated –G).
Beatles: Come Together Meaning –lyricinterpretations.com
"COME TOGETHER RIGHT NOW...OVER ME" refers to the message the Yogi delivered to the band as a group that would supposedly heal the growing rift and dissension between the four members of the band and unite them as a single cohesive unit once again.
If more than just your direct family members support you, i.e., friends, family, donations from strangers, etc., then it can be said that they all came together as (if they were) a family.
If your family isn't on the best of terms, like the Beatles were at one point, you might say: this is what finally brought us together as a family.
Do not confuse this with Tough Love, which is an acceptable practice in my family, when it's appropriate; "requiring them to take responsibility for their actions."
Ironically, your family may 'come together' in order to ensure the application of 'tough love' from all parties (no cheating), with the intent to help them in the long run.
See also: With a Little Help from My Friends