DON'T try it yourself. You'll just end up putting two more dents in the door, even if you get the original one out.
Get a good PDR (paintless dent repair) guy to fix it for you, he will be able to go up through one of the weep holes in the bottom of the door to get at it. If he tells you he needs to drill a hole in the side of the door, find another PDR guy, there's no reason a competent PDR guy would need to drill to get to that dent.
Figure the cost to be $75 -$100.
Where in TX are you?