The story of King Kedara and his daughter Vrinda is not at all related to Kedaranath Jyotirlinga or the mountain.
That story occurs in Chapter 86 of the Krishna-Janma-Khanda of Brahma-Vaivarta Purana and speaks about the creation of the forest of Vrindavana which is where Krishna and Radha enacted their Raas-lila.
Chapter 17 of the same Khanda has the story of Vishwakarma, the deva-architect, building houses and rasamandala for the cowherds of Vrindavana.
Now to answer your question.
The creation of Kedara is highlighted in Chapter 122 of the Nagara Khanda of Skanda Purana.
Indra performs penance to Lord Shiva for the destruction of the Danavas in Himachala. Lord Shiva assumes the form of a buffalo and appears before Indra. Indra asks the Lord to destroy the Danavas.
Formerly, in the beginning of the Manvantara of the first Manu named Svāyambhuva, there was Hiraņyākşa, a Daitya of inordinate
strength. He was of great lustre and possessed the power of penance.
He (and his associates) encompassed the whole world. After ousting the overlord of Devas they appropriated the shares of Devas in Yajnas
by means of their valour.
Thereupon, Sakra took refuge in Gangadvara along with the Suras. In his excessive distress due to the loss of royal glory, he performed a
10-11. Even as the noble-souled one performed the severe penance thus,
Mahādeva himself assumed the form of a buffalo and came out of the
surface of the earth.
He then said to Sakra: "Whom should I tear off (ke=kan, darayami) from the entire hosts of the Daityas by means of this form? O Vasava, O most excellent one among Suras, tell me quickly."
12.. O Lord, tear asunder these five Danavas, namely Hiranyaksa the great Daitya, Subahu, Vakrakandhara, TriSringa and Lohitaksa. If these
are killed, undoubtedly all the Danavas are annihilated.
After killing the Danavas, Indra request Lord Shiva to stay on the mountain (of Himachala) for the salvation of the devotees.
On hearing those words, the Lord hastened to that place where the
important Danava, the extremely powerful Hiranyaksa, was present.
14. All those Danavas saw from a distance the buffalo comparable to a mountain coming on in a frightening form.
The Danavas struck with great effort and their aim was perfect. Yet none of the weapons had any serious effect at all on the body of
After killing the five important Daityas thus, Mahesvara once again went to the place where Sakra was waiting. With great delight in
his mind, he spoke to Sakra fully equipped with the power of penance:
21-22. "Those five Danavas mentioned by you have been killed by me.
Hence enjoy once again the kingdom of the three worlds. O Lord of
Devas, do choose from me another boon too that is desired by you so
that I can hurry back to the peak of Kailäsa."
- O Sankara, do stay here in this very form to accomplish protection to the three worlds and preservation of virtue and welfare.
Śrī Bhagavān said:
- O Sakra, this form was assumed by me in order to slay him (Hiranyaksa) since he could not be killed by other living beings. He
has now been killed by me.
- Hence, at your instance, O most excellent one among Suras, I shall stay here along with this very form accordingly,for giving salvation
unto all embodied ones.
Since Lord Shiva said, "Ke Darayami" when he was in the form of the buffalo, the place came to be known as Kedara.
॥ इन्द्र उवाच ॥ ॥ अहमागत्य नित्यं त्वां स्वर्गाद्वृषभवाहन ॥ अत्रस्थं
पूजयिष्यामि पास्यामि च तथोदकम् ॥ ३१ ॥ के दारयामि यत्प्रोक्तं त्वया
महिषरूपिणा ॥ केदार इति नाम्ना त्वं ततः ख्यातो भविष्यसि ॥ ३२ ॥
O Bull-vehicled One, always (everyday) I shall come from heaven and worship you stationed here. I shall also drink the holy water.
Since you said when you were in the form of a buffalo, “ke dārayāmī" (vv. 10, 11), you shall become well-known by the name Kedara.
[Note: There are two stories told to the sages, one of the Kedara in Himachala and another of the spot where the Lord relocates during the winter. I've only highlighted the former.]