How to do it depends greatly on the final intent and required accuracy. For center to center distances, I usually measure inside to inside distance or outside to outside distance. For same diameter holes, I will zero out the caliper on the hole diameter and then measure the distance. Zeroing out will compensate for any errors due to the lack of a sharp edge, important on small holes. Measuring outside to outside, I use tight fitting pins and again zero the caliper on the pin diameter and then read the center to center distance directly. The two formulae used to calculate the c/c distance are: inside; c/c = i.d + (d1/2 + d2/2) and outside; c/c = 0.d. - (d1/2 + d2/2).
In the case of your part and your final intent, I would approach the measurement differently. Given the repairs and assumed prior use, I would expect egg-shaped holes, in which case, the above procedure gets flushed down the toilet. Having a microscope on my mill, along with a DRO, I would record coordinates at a number of points around each hole and plot them out in CAD. Then I would do a best-fit circle for each of the holes and measure the center/center distance in CAD. Kind of the poor man's version of the CMM in post # 21. If the mating pins/shafts are available, measuring diameters at an unworn area would be helpful.
Reverse engineering a part is always problematic. Even on pristine parts, you have no idea as to where in the tolerance band the part lies. A good example of this was fitting a back plate to a Chinese chuck. In theory, the three mounting holes are equally spaced. However, they in fact were not. They were probably close enough so the hole clearance would allow assembly and may have been within their tolerance but had I made the new back plate to fit the measurements, I would most likely only be able to install the back plate in one position. Add to that measurement errors and you can end up with parts the just don't mate.