If you're sure all needed communication is in place and this colleague is being a "squeaky wheel" for reasons unrelated to getting his work done, then shut him down. Do it politely if you can - you still have to work with him - but more importantly do it firmly.
If you're sure it's warranted, treat his comments/suggestions as unsolicited but well-intentioned advice. Don't get angry, and don't take ANYTHING personally. Don't fall into the trap of thinking that (or wondering if) he has some inside info from David or the client or the team. IF there is some special insight he has - maybe he's worked with this client before, or been in the PM role on a similar project? - then perhaps pay more attention to SPECIFIC suggestions, but trust your gut. Think critically, and keep your cool.
If you're sure he's out of line - I like to use vague, bland, impersonal corporate-speak for this kind of thing:
Thanks for the advice.
David and I are on the same page.
It's handled.
It's under control.
We have open communication channels with the client.
Is there some specific information/help you need to complete your deliverables?
As a side note: I've had people do similar, possibly thinking that I was an easy mark because I was younger, less experienced (in terms of total time in the workplace, not necessarily in relevant experience or in role), female, outwardly mild-mannered, or whatever. Those prejudices exist, and are normalised. But it can also be that someone's a perpetual backseat driver and would give unnecessary input to any project manager. Some people just don't like being in a subordinate role - although they often also don't want to do the unglamourous ongoing work required to be a leader. Often, team members are valuable experts in their own area but don't understand the project manager role, so don't realise their view of a situation may be limited or distorted. And some people just want to feel important/included.
Also, remember that while you DO have the reponsibility to make sure this team member gets his work done adequately and on time, you DON'T have any role in managing or coaching him beyond that. If he's generally a PITA to work with/manage, you only care about that if and when it prevents him or others (including you) from completing their work on the project.