wow. To be honest that's either going to be ugly or very difficult

(i'm talking about the code that should do the trick

)
At first sight, there are 2 different approaches: you can either use sockets or you could use a request-based system.
Sockets
what you need to do is create an XMLSocket (a server) in flash, and allow a server-sided client to connect to it whenever he hovers the link on your page. However, html isn't a programming language, and therefor cannot connect to sockets, so you'll be needing a real programming language such as PHP, ASP, Java or .... You'll need AJAX to send a request to a server-sided script (PHP, ASP or JSP = Java Server Pages), which will then connect to the socket telling the movie to begin to play.
This is an enormous amount of code you'll be needing just to make this easy option on your site, so don't start coding this unless you're 100% sure you need this.
Also, using a socket for this is, let's say, a slight overkill: it's like you're using a bazooka to kill a fly
On the other hand: you have a nice piece of work if you can get it to work, and, if you do it right, you'll have a nice piece of code as well
request-based system
This is the ugly way i was talking about, and you'll probably throw this away immediately.
If you use this, you create a sort of "ping"-server in flash, which will send requests to the server on which a server-sided script will be running that will check if the user is hovering the link. If so the movie will start/stop playing.
Why is this ugly: whenever the user desides not to hover over the movie, you're application will be sending thousands and thousands (like every second) of requests to the server asking if he needs to play the movie or not.
Edit:
Or... I totally misunderstood your question, and actually you want to create a flash application to play movies (you allready have a movieplayer, but you need a link
inside your flash application to start playing it)...
If so, just have a look at "buttons" or "movieclips" and the onMouseOver and onMouseOut events, triggered whenever you hover on the button/movieclip