Water spraying out of drain screw on shutoff valve

Hi trying to do a repair/replacement on a leaking hot water handle for the bathtub, I can get the 2 bolts (pic attached) out of the wall/pipe just fine but cannot get the stem to pull out of the pipe. It will pull out about 1/2 inch but then stops. Now, it wasn't turning off water at all the water pressure would essentially make it pop out that 1/2 inch and it would run full throttle. I've jiggled, wiggled and tried to unscrew but it just doesn't come out. Is there just something simple that I'm missing here? Thanks in advance for any help

Made a rookie mistake when we ordered our new bathroom vanity and forgot to check the position of our plumbing. Long story short, the current plumbing is about 6" to the right of where it needs to be for the new vanity. So either we need a new vanity (or swap the face?) or move the plumbing. The new vanity has drawers where the current plumbing config is and short of shortening the drawer not sure what else to do. Main question is: when I cut into the drain pipe - how do I put in a new tee in that goes to the left? Will the upper vent portion fall down or move? If it doesn't move, how the heck do I get a new piece installed, some kind of T-coupler? No worries on making the cut for the stud. Pics below, thanks! (background is a pretty decent DIY'er, currently at the tail end of a whole house re-model all done myself with dad's help who retired from the biz - his weak spot is plumbing LOL)