I think it’s a shame that we don’t get many interactions between these two. That first episode she appeared was so fun and interesting, and when you think about it from Eri’s perspective—her maybe-almost ex husband is suddenly taking care of the worlds strangest six year old, who is maybe more smart than he should be.
She should take custody of Conan for an episode or two, mostly to spite Kogoro. This would have a very unintended consequences—Sleeping Kogoro would mysteriously disappear, while Conan has to work extra hard on his little kiddie facade around the crime scenes that they are obligated to run into. Plus, Ran would certainly have some complicated emotions. She and Kogoro would have to work together to save Conan from whatever trouble he’s obligated to get into (even though he has it perfectly handled), bringing them together until Kogoro makes some kind of silly comment again.