I achieved something similar with the chrome extension I built, CopyTabs (https://chrome.google.com/webstore/detail/copytabs/obkbjogekcjalnaebheboejhfkamadkg). It is able to open current tabs, selected tabs or windows, in the current chrome user profile, another chrome user profile or another browser entirely.
It doesn't do exactly what's asked as in having https://personal.com open in profile "Personal" and https://company.com open in profile "Business", but if https://personal.com opens in profile "Business" it allows you to move it to profile "Personal".
I made use of
chrome.exe --profile-directory="profileName" to open URLs in a selected profile from a handler that runs on the user's machine.
The command makes use of the internal names of the profiles, for example
--profile-directory="Profile1" instead of
--profile-directory="My Name As Profile".
Hope it's useful.