I read in this website that request should be with that and a clause, not the one with a to-infinitive. In that sense the phrase Request you to send the copy seems to be wrong. If its wrong what would be correct way?
The verb request can be used with a clause to politely ask for something, and with an infinitive to politely ask someone to do something.
Here is a reference to Oxford Dictionaries Online along with a number of usage examples.
1. Politely or formally ask for:
[WITH CLAUSE]: 'The chairman requested that the reports be considered.'
1.1 [WITH INFINITIVE] Politely or formally ask (someone) to do something: 'The letter requested him to report to London.'
I request you to send me a copy of the report is grammatical.