Leaving aside the "correctness" of your scenario (If it works for you it can't be wrong) -
Orlanth took many people into the Storm Tribe from other Groups, so if the Durbandathi is prepared to join your clan, and abide by your laws and customs then this shouldn't cause you a major problem. By rescuing her you have probably already fulfilled one of the mythical requirements (IIRC Heler joined after Orlanth rescued him from Aroka, and Orlanth married Ernalda after rescuing her from the Emperor)
You will, as has been pointed out, have to deal with Durbandaths Agents of Reprisal (possibly even if she remains a Durbandath worshipper, if being rescued by worshippers of an "Alien" pantheon is seen as a religious failure...)
I don't think she need necessarily leave Durbandath to join your clan - it's not like Durbandath is a "traditional" Enemy cult, - although the actions on the Heroquest may have already determined this. An alternative to joining Yinkin would be to try and redeem herself to Durbandath - which could be tricky with no Priests/God talkers to turn to for guidance.
I don't think the absence of a priest/congregation is an absolute bar to continuing to follow your god, although it will make some aspects much harder - lack of support on Heroquests, and even on Holy Days will make contacting your god harder - Divinations and calling for divine aid will be harder. Possibly it will also be harder to improve your magic keywords too?
Another possibility that occurs to me is that a character cut off from their normal congregation, yet determined to follow their god may find that their personal link to the god is becoming stronger as the God calls to them directly and they (are forced to) become their own God-talker
Yinkin is probably the closest match amongst the Heortlings - Presumably they have a common divine ancestor in Fralor(?) As someone else pointed out, you keep any affinities that both cults have in common, and any feats already learned for that cult - I would guess that this suggests that in time the Yinkini in your Clan might learn the Durbadathi feats as your old stories get re-cast with Yinkin in the starring role...
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