Fùmǔ chūguó yǐhòu, jiālǐ de xiǎodiàn yìzhí yóu wǒ dǎlǐ.
Since my parents went abroad, I've been running the family's little shop.
Tips
memory
打 here is not 'to hit' but a general verb of doing, as in 打扫 'to sweep' and 打扮 'to dress up'. 打理 is everyday and practical: you 打理 your hair, a garden, a household or a small business. For running a company, 管理 is the formal word.