Daily conversation : Japanese greetings

Recently, I try to translate Japanese what I say into English in my head.
Especially I wonder how to say in inflows these words.

“Ittekimasu” ( I’m going. / See you later.)
“Itterassyai” （ Have a good day / See you. ?）
“Tadaima” ( I’m home. ? )
“Okaeri” ( Welcome back ? )

These greetings are Japanese culture, so should I change my thinking in the first place?
I’m worried like that, but my 1-year-old second-born son says “Bye bye!” when he sends me out.
→These are a Japanese specific expression.
I guess I should change the way I think of it in the first place.

I guess it’s because he watches English films (DVDs) for leaning English.
My kids are good at adapting rather than I am.

最近、自分が話した言葉（日本語）を、英語だとどんな表現になるのか、考えるようにしてます。
しかし、これらの挨拶を、どのような言葉で置き換えるのか、よく悩みます。

「行ってきます」( I’m going. / See you later. ?)
「行ってらっしゃい」（ Have a good day / See you. ?）
「ただいま」( I’m home. ? )
「おかえり」( Welcome back ? )

これらの挨拶は、日本的な文化なので、そもそもの考え方を改めた方がよいのでしょうか？

私はそのように悩んでいるのですが、１歳の次男は、私を送り出す時、「ばいばい！」と言います。
（多分、幼児向け英語DVDから学んでいる）

案外、子供たちの方が順応性が高いのかもしれません。

修正内容

But, I often wonder what words to replace these greetings.
→Especially I wonder how to say in inflows these words.

“Ittekimasu” ( I’m going. / See you later.)
“Itterassyai” （ Have a good day / See you. ?）
“Tadaima” ( I’m home. ? )
“Okaeri” ( Welcome back ? )
→ 合致する英語表現がなく、時と場合によるので一概には言えない

These greetings are Japanese culture, so should I change my thinking in the first place?
→These are a Japanese specific expression.
I guess I should change the way I think of it in the first place.

I’m worried like that, but my 1-year-old second-born son says “Bye bye!” when he sends me out.
→I have been thinking so.
However, my son says bye-bye to me when he sands me out( when I am leaving)

(Maybe he’s learning from an English DVD for young children.)
→I guess it’s because he watches English films (DVDs) for leaning English.
Surprisingly, my kids are more adaptable than I am.
→My kids are good at adapting rather than I am.