I'm just too overwhelmed by taking care of my kids and my English lessons, that I feel I just don't have time to take piano lessons.
I'm just too caught up with taking care of my kids that I feel I don't have time for piano lessons.
何かに誘われた場合等に、何かに急がし過ぎた場合、「〜でいいっぱいいっぱいです」と言いたいならこのようは自然です。
I'm just too overwhelmed by ○○.
I'm just too caught up with ○○.
I just don't have enough time, due to ○○.
多分、「I just don't have enough time for ○○」と伝えたらいいと思います。「○○のための時間がない」という意味です。
例文:今は子供の世話と英語の勉強でいいっぱいいっぱいです。
I'm just too overwhelmed by taking care of my kids and my English lessons, that I feel I just don't have time to take piano lessons.
I'm just too caught up with taking care of my kids that I feel I don't have time for piano lessons.
I just don't have enough time to take piano lessons, with taking care of my children and taking English lessons.
上記の例文に「I feel I~」を入れたら、もうちょっと和らげるように断ります。
英語頑張りましょう:)
I have my hands full between raising my child(ren) and studying English
I'm busy juggling child rearing and English studies
I have my hands full between raising my child(ren) and studying English = 子供を育てるのと英語を勉強するので手がいっぱいです
I'm busy juggling child rearing and English studies = 子育てと英語の勉強の二つに追われている
Juggle = ジャグリング、次々と物を宙に投げて受け取る芸
Child rearing =子育て