What are the instances where Krishna promised that he would return to Vrindavan either himself or through representatives like Uddhava?
Krishna promised such thing when he left for Mathura with Akrūra:
गोप्यश्च दयितं कृष्णमनुव्रज्यानुरञ्जिता: ।
प्रत्यादेशं भगवत: काङ्क्षन्त्यश्चावतस्थिरे ॥ ३४ ॥
तास्तथा तप्यतीर्वीक्ष्य स्वप्रस्थाने यदूत्तम: ।
सान्त्वयामास सप्रेमैरायास्य इति दौत्यकै: ॥ ३५ ॥
[With His glances] Lord Kṛṣṇa somewhat pacified the gopīs, and they also followed behind for some time. Then, hoping He would give them some instruction, they stood still.
As He departed, that best of the Yadus saw how the gopīs were lamenting, and thus He consoled them by sending a messenger with this loving promise: “I will return.”
There are few instances when such promise was made.
First one when Krishna was leaving for Mathura:
tās tathā tapyatīr vīkṣya sva-prasthāne yadūttamaḥ | sāntvayām āsa sa-premair āyāsya iti dautyakaiḥ ||
As he departed, that best of the Yadus saw how the gopīs, were lamenting, and thus he consoled them by sending a messenger with this loving promise: “I will return.” SB 10.39.35
Another instance, Krishna speaks to his father Nanda. This occurs some days after Krishna kills Kamsa.
yāta yūyaṁ vrajaṁ tāta vayaṁ ca sneha-duḥkhitān | jñātīn vo draṣṭum eṣyāmo vidhāya suhṛdāṁ sukham ||
Now you should all return to Vraja, dear father. We shall come to see you, our dear relatives who suffer in separation from us, as soon as we have given some happiness to your well-wishing friends. SB 10.45.23
Another instance, Uddhava brings Krishna's message to the residents of Vrindavan.
hatvā kaṁsaṁ raṅga-madhye pratīpaṁ sarva-sātvatām | yad āha vaḥ samāgatya kṛṣṇaḥ satyaṁ karoti tat || āgamiṣyaty adīrgheṇa kālena vrajam acyutaḥ | priyaṁ vidhāsyate pitror bhagavān sātvatāṁ patiḥ ||
Having killed Kaṁsa, the enemy of all the Yadus, in the wrestling arena, Kṛṣṇa will now surely fulfill his promise to you by coming back. SB 10.46.35 Infallible Kṛṣṇa, the Lord of the devotees, will soon return to Vraja to satisfy His parents. SB 10.46.34