Hi,
For us to better understand your set-up, can you elaborate a bit more on "setup https inspection in the environment where we have 3 separate domains" - more on the last part of the phrase.
In our company where we implemented HTTPS Inspection, we have a Root CA (smth.int) that has 3 sub CA's like ( regionEU.smth.int, regionNA.smth.int and regionAP.smth.int) . But the delegated sub-CA we installed on the CheckPoint, was generated by the Root CA (smth.int) so all clients from the regions will trust it.
Hopefully it will clarify your question, but please come back with the asked details.
Ty,