阿部さんの話題で彼はお爺ちゃんが元総理で政治家になるべくして生まれてきたんだ、と言いたい。He was born to be a politician because his grampa was the Prime Minister and his father was also a politician. He was born in a political family.
「政治一家に生まれる」は
be born into a family of politicians
be born into a long lineage of politicians
のように言えます。
lineage は「家柄・家系」という意味です。
例：
He was bound to be a politician because his father was in politics and his grandfather was the former Prime Minister of Japan. He was born into a family of politicians.
「彼の父は政界の人、祖父は日本の元総理だったので、彼は政治家になる運命だった。彼は政治家一家に生まれた。」
be bound to be ... で「…する運命にある」
ご参考まで！
カナダ 
