POV Rhaegar
Charming nobility is a tedious thing particularly if the noble in question is one Oberyn Martell, Prince of Dorne. Its irritating to grin and bear all the passive aggressive remarks about rejecting Elia Martell as a bride or feigning ignorance to all the invitations of sharing a bed. Rhaegar himself didn't have any strong opinions about men attracted to men or women attracted to women, whatever works for them is their business and none of his. And Rhaegar could see for all of his flamboyancy and seemingly inane chatter that Oberyn is working Cousin Robert and Rhaegar for information, carefully inquiring about Ned Stark, information which Robert freely gave away but not the information Oberyn was searching for. For Robert his friend Ned is honor incarnate, Just as Father himself with boundless mercy for children, women, friend and foe alike, dutiful and intelligent.
Rhaegar wondered whether Robert is in love with Ned. His cousin seemed to enjoy a woman in his bed too much for that, what with a bastard daughter in Vale and working enthusiastically in making more, but who knows a mans heart, I certainly always don't know mine. But Oberyns interest is telling, the man wanted know whether Ned was a schemer, a player of Game of Thrones, most probably Ashara and Oberyn are working together to unravel the knot that is Eddard Stark, probably at Dorans direction, what with Ashara keeping Ned occupied all day and Oberyn doing the same to Robert and Rhaegar himself.
Rhaegar wished them well in the endeavor, Rhaegar has known Ned for years and hadn't been able to make sense of all Neds actions. The man works in convoluted ways yet insists that he only walked the straight path. And it feels to be true too, as long as Ned explains it, everything is logical, but once away from the mans company, all of it becomes a tangled mess.
Thinking of Ned, the information he provided about Lannisters is concerning. Not just the information itself, the quality of information is too. That quality of information just doesn't fall into someones lap, it takes a deeply embedded network, with long reach and trained spies. Which is concerning because the North and House Stark did not have much of network just two years ago and they didn't seem to have one now. Oh, they made use of information network maintained by merchants and bards throughout Westeros and Eastern Essos, but everyone uses that, anyone with a bit of coin can tap into that, there is no shortage of merchants and bards two timing as information brokers. The merchant network is slow, inefficient and not very accurate about information of Nobles and their Houses, but it is an excellent tool to take pulse of sentiments and movements of the masses and general news.
It is not very difficult to start a basic spy ring going, most use whats already available, tap someone who is in the general vicinity and has some contact with the target, someone with need of coin, a bit ambitious, clever enough to know betrayal of their employer will get them a sharp knife in the back or a hot knives in a damp dungeon, but not smart enough to understand most spies end up at the wrong end of a short rope anyway, make them do the spying and assign a handler to keep an eye on the intrepid spy or spies, the handler should be in reach to pass information regularly enough. The Handler will have additional duties to liaise with local information brokers and sources such as tavern keepers, inn keepers, dock masters, gate guards, sneak thieves, smugglers and other criminal elements discreetly, and to collate all information and send it securely to the spy master who in turn will manage the network and report the information to the employer.
Sending the information is not that difficult either, with the exception of Winterfell, every Great House of Westeros have a town or city nearby their Ancestral Seat, Casterly Rock has Lannisport, Red Keep has Kings Landing, Sunspear has Shadow city, Stroms End, Highgarden and Riverrun have nameless towns within five miles, even Pyke has a ramshakle town outside its walls. Though Winterfell has Wintertown, it wasn't much of a town and not even fully occupied outside of winter. These towns are important because, every sizable town or city in Westeros has a Maester who keeps ravens, which can carry messages between every other town or city(this arrangement came to be because Merchants petitioned for it during reign of the Old King, for exchange of information so that merchants can find better markets for their goods), Maesters who for a bit of coin for their discretion allow Handlers to send reports to their Spy Masters. It would have been frankly quite impossible to run a spy network without these Maesters and their ravens, because a spy or a handler can never use ravens of a Castle, that's an easy way to get caught, to be tortured and get dumped in sewage with their throat slit.
All of this is basic spy work and no true player of Game of Thrones stops at basic, there are campaigns of misinformation, identifying and turning the spies, spying on spies, their own and others, using bottleneck of Maesters to identify handlers, double crosses and triple crosses, sabotage, games of cat and mouse between spies, shadow wars between rival networks, complete elimination of spy rings during wartime, assassinations and so much more. That is to say if Starks have a network then ripples of it would have been felt by every other network and masters of those networks. That left magic as only other option.
Even then, the limitations of warging as explained by Ned assure that mechanics of spying through warging doesn't much differ from normal spywork. Ned could have lied of course, but that seems absurd. Rhaegar is sure Ned has a ruthless streak mile wide when required but the man seems to abhor lying and has no talent for it. That Honesty of Ned Stark has a strange magnetic quality to it. And that leaves some loophole of warging that Ned never explained. Rhaegar is sure if he asked Ned will answer him truthfully, but Rhaeger does not want to do that, his friend deserved his secrets and any knowledge he wanted will be made known to him once he married Lyanna Stark anyway. So why dig for something when it will be placed in his hands anyway.
That leaves him with Lannister Twins situation, even thought of it is enough to raise bile of disgust in Rhaegars throat, it may seem hypocritical for a Targaryen to be disgusted by incest, but its precisely because he is a Targaryen that Rhaegar is disgusted by it. For every happy incestuous marriage in his family, there are twice or thrice as many unhappy ones. And happy ones seemed to be somehow twisted to Rhaegar, just how narcissistic one has to be to happily fuck their own brother or sister, these Lannisters being twins only somehow made it so much worse.
Anyway if these incestuous siblings were backwater nobles then this situation wouldn't have mattered much, but these are Lannisters, they are key to stability of Westerlands and a stable Westerlands is a necessity for stable Westeros. Rhaegar momentarily thought to use this situation for his personal benefit, as blackmail the knowledge that next Warden of West is a sisterfucker is powerful leverage, but that's narrow minded thinking. Rhaeger is poised to one of the most powerful persons in the Known World anyway, he needs more stable Westeros than more personal power, to face what's coming. So how to resolve this? What to do?