Are My Component Values (A, B, C, D) Correct for Hall Sensor Relay on 12V Automotive?

Hello,I'm very new to electronics, and I seem to keep burning out my switches  while testing my setup.  I'm trying to use a hall effect sensor to switch a relay on a 12 Volt automotive system. This is replacing a simple momentary switch.I found  a 9 Volt schematic, but I'm unsure of which components need to change for use with 12V. I've included the original (left) compared to my modified diagram (right). Are my values for A, B, C, and D correct?Many thanks for any help or advice!!
-Tim

First thing is to check the data sheet for the hall effect sensor.
https://www.elecrow.com/download/A3141-2-3-4-Datasheet.pdfFortunately this part has a wide supply voltage tolerance but maximum output current is 25 mA. Since you are using this to turn on a 2N3906 (which has about 0.7V between the base and emitter) you need to drop about 11.3 V => A should be larger than 11.3/25m = 452 so the 610 you have there should be good. that will give you about 18mA which should be more than enough. 
The questionable thing on your diagram is the LED, resistor, and relay. What is the input rating of the relay? The 2N3906 has a max output of 200mA so you want to stay under that. Also if you are using a 12V relay, the drop across the LED and resistor might be enough that the relay won't turn on.

Elizabeth, thanks so much for your reply!!The relay is a general purpose 31579-04, but I'm having a hard time finding any real info on it. I'm not 100% sure, but I think it needs 6.6volts to switch. I'm reading that the 1k resistor in my schematic is supposed to be a "pull up" type to make that happen. I'm also reading that the 2N2907 will handle more current than the 2N3906, so I may have to go with that transistor.

Tim... As Elizabeth says, the LED/Resistor / Relay are probably what's causing your problems.
1. Don't put the LED in series with the relay.  The relay (the type you have drawn is an automotive relay which probably  takes 100mA or more, this would burn out a LED, though with your resistor in series the LED would light but the relay might not operate....2. As Elizabeth says, the 2N3906 is not a very beefy device, I'd use something bigger in a TO-39 case (2N4406 springs to mind but there's probably better newer ones - look for a transistor with a 500mA or more collector current (Ic) rating.3. When you're switching a relay (which is an inductor) with a transistor, ALWAYS put a reverse biased diode across the relay coil.  When you switch the transistor off suddenly it can generate a back-emf of a few hundred volts on the inductor.  Pop goes the transistor.4.  The Hall sensor can work on 12V.  If so you should wind up with a diagram like this:
I have:1. Used separate feeds to the relay and the LED though they are fed from the same transistor.2 Used a 2N4406 - datasheet here.3. Used a 1N4001 to catch any back emf from the relay switching.  Beware - if you get this the wrong way round you'll blow the 2N4406!4. Left the base resistor at 510 ohms, though you could probably increase it up to 1K without a problem, depending on the relay current.  the Base-Emitter resistor will probably be OK as a 2K2 , again you may have to experiment.  I've increased the LED resistor to a 1K which should give you around 10mA through the LED.

David-Thanks so much for your help & for making me a new diagram! I finally tracked down the components I needed, and so far my tests have been successful. Now to wire it up for some field tests.Thanks again!!Tim