Most 12V voltage regulators (12V is a good voltage to use) have a maximum voltage input of 35 or 36 volts. You should leave yourself some headroom for voltage spikes and surges, so that leaves out using the standard 78L12 type of regulator.
You can use something like a TL783. As you will notice from the datasheet, it has a maximum current output of about 700mA. This is really not a problem though. You simply want to put a large capacitor (say min. 4.7uF up to 10uF) on the output of the regulator, and also another 1.0uF to 4.7uF over at the charge pump capacitor for each drive chip. I would also recommend a couple smaller bypass caps (ceramic) over at the input to the diode (Vcc) for the charge pump. The 2A that the IR2110 requires is for a very short amount of time while it is turning the FET gate on. It is not a continuous rating, so the 700mA from the TL783 will be fine. The actual drive current(charge) will come from the caps. You may need to heatsink the TL783, (depending on the actual input voltage and current draw), so watch that.
With the IR2110 you need to be very careful that both the high side and the low side are not on at the same time, or current will shoot right through both of them. Since it takes time for the FET to turn off, you need to build in a "dead time" between turning off one gate and turning on the another. If your FETs get hotter than it seems like they should, make sure you aren't getting any shoot through. If they blow up, then you definitely need to check for shoot through. Buy extra FETs while testing just in case.
The charge pump method of building the voltage on Vb requires that at some time the Vs line will be pulled low (through the LO side FET) to charge the capacitor. Thus, if you are using PWM to drive the gates, make sure you do not leave the high side on 100 percent of the time.
When rating your FETs take your maximum current draw and multiply by 3 to get the rating of the FET you want. If you need 10 amps, then use a FET rated for 30 amps. For voltage, if you are going to be using 36V, then use a FET with a an 70 or 80 volt rating to account for voltage spikes. Make sure the FETs have good heatsinking.