‘Please check your forms thoroughly. Please check your coursework throughly.’
‘Please check your forms and coursework work thoroughly.’

I know it seems a bit long-winded to use option one instead of option two but is the use of option two actually grammatically incorrect?

It does seem a little long-winded, but it’s perfectly fine to use two sentences when one would do ^^.

So its grammatically correct, just long-winded?

Yeah, exactly :).