I have both DLC's installed legit from the PSN before it went down.
I noticed when working with some of the sunnie mods (weapon mods, specifically) that I lost access to the Black Emporium (but not dog). First time it was there but with no name and the quest letter was invisible on the desk; clicked it and it marked it as read, but did nothing. Second time, the location just wasn't there.
So there may be some incompatible mods causing issues with the DLC.
When I removed the sunnie mod as well as rewards.gda and some others, it worked fine, and it's working well with my current mods.
So for the sake of DLC exploration, I'd recommend not using any other mods when testing and trying to get it to work.
Haven't messed with the Exiled Prince with mods yet, but it's been in my quest log and I haven't seen any issues.