Friendship
Amity
noun, verbal noun
If a parent is friendly enough you can form a friendship with them, not just a kid/parent bond.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
親睦を深めるためのパーティーを準備しています。
We are preparing for a party to strengthen our friendship.