You have a variety of options you can use to accomplish most of your questions:
1. How can we provide secure access to these non-corporate users who are domain joined to other domains? (We can not join these others domains to ISE)
-You could setup client provisioning to force the non-domain joined computers to essentially be forced to download the ISE posture module or a temporary module that you can use to run scans/checks on these hosts. You will have to figure out a way to default these non-domain computers into a network that is restricted and that has a separate AuthZ profile that forces them to client provisioning portal.
2. We want to make sure only these non-corporate machines (joined to other domains) are allowed network access and not any personal laptops.
-You can leverage posture checks to determine this. One example, if you are aware of the other domain names you could do a registry check to determine if a certain string exists and if not deny access to personal laptops that technically would not be a part of a domain.
3. We want to also check if these non-corporate machines have a valid Anti-virus as a posture assessment condition.
-You can leverage posture checks here again to determine if a certain AV service is actively running.
4. These users have domain credentials but we dont want them bringing their personal laptops and using those on the network.
See answer to question 2.
5. Can we use their domain to profile these non corporate users some how? How can we differentiate, Corporate machines with non corporate machines?
-You can utilize the AD probe assuming that you have your NADs configured as device sensors. Using that probe you can utilize the attribute ADHostExists EQUALS True or False. Another example is if you are aware of the other domain naming conventions you could utilize the hostname string attribute.
Good luck & HTH!
