Time to turn on the Skept-o-vision. Do his "feelers" (ew) check out? Have you met any of these contacts, or is he controlling all communication? Can you verify his friend's existence online?
If you want to try to find out just how fast you should be backing out of hug's reach — is he volatile or just cluelessly optimistic? — mention to your cousin or her sister how much you appreciate Ex's efforts to help you. Then watch like a hawk for the reaction. Speaking of hawks, if I were your mom, I'd want to know.
In any case, you should restrict further networking with him to phone or email. If he balks or tries to guilt-trip you, you're done. That's not how networking works. And start cultivating leads elsewhere: LinkedIn, networking events, an internship. I guarantee soup-and-salad with this creepy ex-cousin is not your only entree into the field.
Karla L. Miller writes an advice column on navigating the modern workplace. Each week she will answer one or two questions from readers. Miller has written for and edited tax publications for 16 years, most recently for the accounting firm KPMG's Washington National Tax office. You can find her on Twitter, @KarlaAtWork.