Before reading TeGGeR's response, we took off the rear wheels and
checked the drums. The drums are not turning smoothly. It's almost
like they were machined off-round a little bit or something. We called
the shop and they said they would turn them for free, as they should
not be that way.

So, that's what we are going to try first. My father-in-law test drove
the car after he finished the complete front end, and it did not
shudder at that point. So we are assuming it's a rear issue.