I had the same situation with a PM of one of my places earlier this year. But I googled some places and copied the links into an email for her to follow up on. I stood my ground and made sure that extra quotes were provided.
Really annoys me that all they will use is there trades, who are more often than not very expensive.
No - doesn't sound too demanding. Nothing wrong with requesting a couple of quotes. It's a pity they don't have connections - I'd assume most PM's would have builders/handy men/women they know.