Amplifiying PWM signal to 10v analog
Make a 0 to 5 volt analogue signal by the appropriate filter (op-amp sallen key or RC etc.) and then use a non-inverting gain of 2 op-amp circuit to follow. You should be able to find an op-amp that can run from 12 volts that has a near-rail-to-rail output capability for this. Pay particular attention to the ability for it to get close to 0 volts. If you were already considering using a sallen key op-amp filter, you can build it with a natural gain of +2.
This type of circuit will only deliver a moderate output current. If you need to drive more than 10 mA there are other options.