Intentionally pitching at the batter is an unsportsmanlike act and grounds for ejection. The umpire needs to use his best judgment in determining if the act is intentional or malicious. If the act is judged to be intentional, the best course of action- from a game management standpoint, to prevent any escalation or retaliation- is to eject on the spot. But I'm going to need some pretty strong evidence to convice me that the act was intentional.
Hit batters are a part of the game. Pitches get away, pitcher's lose control and batters can (legally) crowd the plate. There is no standard rule that says a pitcher must be removed if she has hit "X" number of batters and certainly no rule directing the umpire to order a coach to remove a pitcher for hitting batters.
I will note that I have seen some local leagues add a rule that a pitcher must be removed after hiting, say, three batters. That is not a standard rule found in any of the major sanctioning body's rule books. Such misguided rules are usually added under the umbrella of "safety". They effectively take away an umpire's judgment and force all hit batter's to be weighed equally. A pitch clocking the batter in the helmet must be regarded the same as a perfectly legal pitch that is slightly inside and barely brushes the batter's jersey. Such a rule can actually encourage batters to allow themselves to be hit, as the incentive is there to get a tough pitcher removed from the game.
Issuing a warning that "the next hit batter gets your pitcher removed" is not a recommended game management technique, for the same reasons that putting a limit on the number of hit batters noted above can backfire. An umpire making such a warning is over-stepping his bounds. If it's judged to be intentional, eject and end the problem. If it's not intentional, it's just a part of the game and there are no grounds for removing the pitcher.
As for crowding the plate, a batter may position herself anywhere as long as both feet are entirely within the batter's box. The box is six inches away from the plate. If the batter is closer than that the umpire should call time and instruct the batter to properly position herself before allowing the pitcher to pitch.
If the batter is hit within the strike zone, or in front of the plate, thus preventing the pitch from entering the strike zone, as cshilt notes above the correct call is dead ball, strike to the batter and no award of first base.
