I'm going to work hard at my job, so you work hard at school too.
We'll both work hard, mommy at work and you at school.
この場合、次のような言い方ができますよ。
ーI'm going to work hard at my job, so you work hard at school too.
「ママもお仕事頑張るから、あなたも学校頑張って」
to work hard で「頑張る」と言えます。
ーWe'll both work hard, mommy at work and you at school.
「ママはお仕事で、あなたは学校で、どっちも頑張ろうね」
ご参考まで!