Man, it's always amazing how Kogoro always find an explanation for the weird things that Conan found.
huh? why he called the older womam "mother-in-law"? should not he call that mother?
This is a typical mistranslation.
The word for step-mom and mother-in-law are the same in Japanese, so you need the context to correctly translate this.
And as you said, he should have said "step-mom" on the first page.
Meanwhile, it's correct for the step-mom to call the grandma "mother-in-law" on the later page.