At what point during product developoment were these critical characteristics determined. (Are the dimensions listed as critical on the drawing?) I can understand your suppliers attitude if you are coming in after PPAP and asking the supplier to control dimensions that were not previously discussed during product development, without some help with the commercial aspects.
If this was discussed during development, I agree that they really have no choice but to implement. You may find that, since the organization is small, you may have to offer assistance with training and implementation to get them started. If they do not chooses to implement, have them 100% the dimensions and let them decide which approach is the most cost effective.
A second approach if you have not yet given PPAP approval is to hold this until you are satisfied that the control plan and PFMEA contain control charting to address the area where you have designated critical characteristics or high RPN values.
One last question, When you were selecting this supplier, did you assess their quality system to insure they could satisfy all you needs, including SPC requirements?