You don't need 10 miniature cameras unless you have the budget to buy them or the crew to operate them. The only way to do it is to move the camera from person to person showing each of their hands (I thought the first rule of poker was not to show your hand?) so why does your brother want to see everyone's hand?

If you cannot stop the action or control it (I presume it's a real game and therefore you can't shout CUT every few minutes - or can you - while you set up the next shot) then you will have to just move around the players as quietly and as unobtrusively as possible.

Download a 30 day trial of Adobe Premiere Elements 3 or 4 and that will allow you do all the things you want, the 30 days should be long enough for you to capture, edit, add graphics, maybe some music (copyright free if you intend to show the video outside your home) and then burn it to DVD. I don't know about it being 'slick', as this is your first time to produce a DVD, treat it more as a learning the ropes exercise.

__________________
Better than a poke in the eye with a pointy stick any day...