How do you properly ground a digital pot and an op-amp?
Suggestion: 

You don't really need the digital pot, the op amp to amplify the pot's output voltage, or the nice multicolor marker lines, to do what you require. 

Explanation:

"DIMMING CONTROL (OPTIONAL) 1 ~ 10VDC or PWM signal : 100Hz ~ 3KHz" means the dimmer can be operated either by varying a DC analog voltage (Solution 1 below), or by varying only the duty cycle a PWM signal at your choice of frequency in the 100 Hz to 3 KHz range (Solution 2 below). 



Solution 1:

Use a 10 volt regulated power supply such as a wall-wart, or even just a 9 Volt battery, and a potentiometer, in the following configuration:



A 9 Volt battery would be good enough for general use, the only constraint being it would reach only up to 90% of full brightness setting of the dimmer.

The center wiper contact of the potentiometer goes to the analog dimming input pin D+, and the negative side of the battery connects to one of the end contacts of the pot, and to the D- pin of the dimmer.



Solution 2:

Connect one of the PWM outputs of the Arduino, for example pin 3, 9, 10, or 11, to the PWM input pin D+ of the dimmer, and connect one of the GND pins of the Arduino to the D- pin of the dimmer. The default PWM frequency of the Arduino is approximately 490 Hz, within the acceptable range for your dimmer. 

Set the dimming level you want, on a scale of 0 to 255, using AnalogWrite() in an Arduino sketch. By not changing any default frequencies, the operation of the Arduino will not be affected in any adverse way.



EDIT: Added Solution 3, from a Meanwell dimming thread on a discussion forum.

This solution is useful for Meanwell dimmers which only support the 0-10 Volt analog dimming method, and do not have a PWM option.



From the relevant post: This circuit will let you dim a D driver with the PWM outputs from the Arduino.



Notes:


The dimmer input Ground pin referred to above should be one of the pins of the control input connector of the dimmer - NOT the neutral line of the mains, if the dimmer you refer to is used for mains dimming
A link to the datasheet of the dimmer will be useful to determine whether the dimmer control input needs some form of optoisolator - should not be the case, but better safe than sorry
Update: Meanwell dimmer controller D+ and D- input pins do not need to be externally isolated.
Assumption: Your concept of using the op-amp was to be able to achieve a 10 Volt signal range without providing any 10 Volt power supply... That doesn't work, the op amp itself requires a 10 volt supply at the minimum, to be able to provide 0 to 10 Volt output.
Assumption: Your use of the digital potentiometer was purely for the purpose of programmatically controlling voltage from a microcontroller. In that case, the analog potentiometer voltage divider shown above in Solution 1 can be used as an input to the microcontroller, powered from the microcontroller's Vcc pin instead of the battery. The PWM output as in Solution 2 would then remain as stated, for actually controlling the dimmer.
OP mentions in a comment that the PWM dimming works thus: 100 Hz = supply off, 3 KHz = max brightness. The datasheet for the Meanwell ELN-30/60-XXD(P) contradicts this, stating:

In other words, the PWM duty cycle defines the brightness, regardless of the PWM frequency, within the allowable range of 100 Hz to 3 KHz.