First question I have to ask is: Is the domain of the Sister Site added as an Internal URL? If both sites track into the same global suite, this is how it should be... but then, this also will not track as a referrer (intentionally).
I assume this is the case by your statement "What dimension do I use to see the referrers within Internal in Workspace?" but I am just confirming.
If this is the case, then your Marketing Channel shouldn't trigger, it will be the Marketing Channel that brought users to the sister site that will be recorded... same with Referrer... your internal domains won't be available (at least out-of-the-box).
So if you need to look at your current state, you may have to use Flow / Fallout / Segmentation (Sequential) to try and get some information.
Going forward, you might want to build-in some sort of custom "Internal Campaign" tracking (using a visit expiry eVar - and not to overwrite any of your external campaigns, since you would want to make sure that external efforts to drive traffic aren't lost).
You could also create a custom hit expiry eVar (I say eVars simply for the 255 character limit as opposed to the 100 character limit that props have) to track your referrers (internal or external) so that you can see specifically how the users are flowing... but of course, on the conversion, that would be the previous page... so you could also look into a Visit expiry eVar that only tracks the referrer when it doesn't match the current domain of the page... this should act similar to the Adobe Referrer, but won't exclude your internal urls.... but it won't trigger on every page, only when the user comes from A to B, or from B to A, or from C to A, etc....