Electronic – arduino – create a stable 0-10 V DC output from a 3.3V PWM signal (arduino/esp8266)

More questions than answers, but the answer should emerge as you answer these questions:

MCP4922 datasheet here.

Please provide complete circuit diagram of what you are ACTUALLY doing?

Try feeding DAC Vdd also from Vref.

Note that DAC Vdd needs to be such that SPI signals provide valid high and low logical levels at both ends of SPI link. This MAY be able to be accomplished when Vdd_sender <> Vdd_DAC but it is usually better if they are the same.

What is load on each DAC output?

What voltage is "my power rail"?

What voltage is DAC Vdd?

What current can your Ref supply?
NB: as it is a shunt regulator its current feed capability at 5V depends critically on its feed resistor.

Is ground connected correctly in all cases?

ADDED

This is ambiguous:

• ... (DAC) vdd should be the same voltage as my arduino They both run at 5v. The psu rail is also at 5v. Its can supply upto 10ma. It's the same one I post posted about earlier on (LM336). However I didnt have the resistor size you suggested so I reapplied ohms law and came up with 8.2k. According to my dodgy math it's 1ma current.

The circuit diagram that you posted is what you are APPROXIMATELY trying to copy.
You have changed a number of things.
You are using words like 'power supply', "It can supply", "psu rail" etc but it is unclear what reference is to which device and what connections are really made. I could probably have a reasonably good guess at what you mean and what you think you are doing BUT I may get it wrong and YOU may have got it wrong. If you post a diagram of EXACTLY what you think you hav done then we can tell you what you should see and we can go from there. As is there are too many uncertainties. You need to show Arduino as a block diagram, basic Arduino powering with voltages, SPI connections, ALL DAC power and signal connections and regulators and resistors and connections. In you other post you mention a 12V supply - is this still supplying the Vref regulator. Don't just tell me - show it on your diagram. A hand drawn diagram is fine as long as it is clear, well labelled and unambiguous. It need only include the circuitry relevant to the question, but more is OK.

165k input impedance is NOT a problem. This just shows that the DAC load is light compared to drive capability or other loads, which is good.

From the block diagram in the datasheet, you can see that the current sensing is influenced by the output stages of the H-bridge. This means that when you use PWM to drive the motor, the Sense voltage will vary with the PWM signal. The voltage across the sense resistor is proportional with the current through it, which in turn depends on the voltage across the motor's induction. During the positive period of the PWM signal, the current will be 'slowly' increasing whereas during the negative period of the PWM signal the current will be 'slowly' decreasing. In practice this will look a bit like a triangular wave and that is the noise you measure.

The solution is to make sure that you synchronize the sense voltage measurement with the PWM signal. For example you can attach an interrupt to the timer that is used for the PWM signal and it requires a fair bit of digging into the microcontroller's datasheet (and some trial-and-error) to figure out how to realize that. Another option is to connect an interrupt pin to the PWM output pin, which may be simpler to start with. It can be done, though you might need to lower the PWM frequency (to fit the ADC conversion within the PWM duty cycle), directly program the hardware registers (Arduino libraries are slow) or use some assembly.