I have to say~东家出西家进not is "someone is too busy" it means: drop in A family, and stop by B family,in a word,just drop around~ 忙些家长里短的事：“ be busy talking something trivial or doing something trivial in daily life." these are the right translation.wish it could be adapted.

1.东家出西家进（Someone is too busy.) 2.家长里短 jiā cháng lǐ duǎn (Refers to something about the family daily life.) So,the sentence means someone is too busy to do something Trivial just like something about the family daily life. (Hope that helps.)