请 is also a verb, meaning ‘to invite, to politely request’. When both 请 and 你 are used in an imperative sentence, ‘请你 + action’ may have a different connotation from ‘你请 + action’.
你请 or 请你 can imply an invitation:
A，wáng lǎo shī ，nín hǎo ！nín qǐng jìn lái zuò 。……Qǐng nín hē bēi chá 。
Ah, Teacher Wang, how are you! Please come in and have a seat. . . . Please have some tea.
When a command (but not an invitation) is given in a polite way, 你请 is not appropriate.
Only 请你 is proper in this context:
Wáng ：qǐng nǐ gěi wǒ qù yóu jú mǎi jǐ zhāng yóu piào 。
Wang: Please go to the post office and buy some stamps for me.
Dīng ：hǎo ，bú guò qǐng nǐ xiān bǎ mǎi yóu piào de qián gěi wǒ 。
Ding: OK. But please give me the money for the stamps first.
When a command is given in a polite way, 麻烦你 can be used to replace 请你. 你 is not optional.
Má fán nǐ gěi wǒ ná bēi shuǐ lái 。
Would you please fetch a glass of water for me?
 Yip, P. C., Rimmington, D., Xiaoming, Z., & Henson, R. (2009). Basic Chinese: a grammar and workbook. Taylor & Francis.