What is the source of the 'Dadhi-VAmana' Form of Sri Vishnu? Why did He take this particular Form?
Lord Viṣṇu took the form of Vāmana to subdue the pride of King Mahābali Cakravarti.
Dadhi, is the Sanskrit word for curd. (Source for the translation)
दधि (n.) dadhi - curd
It is believed that offerings of curd and curd-rice are very dear to Lord Vāmana. Hence, the name Dadhi Vāmana.
It is interesting to note that there is also a Sālagrama Mūrtī called Dadhi Vāmana Sālagrama.
This Sālagrama Mūrtī, aptly has small white spots on it. These are identified as tiny dots of curd.
The Mantra for this Sālagrama reads:
With a half-Cakra on the top, and having spots of curd on it, Vāmana, with with a reddish and bluish hue, they say, is DadhiVāmana.
There is also a Mantra to this form of Vāmana called DadhiVāmana, called the DadhiVāmana Stotram. You can find it at http://www.hithokthi.com/viewstotra.php?g_id=8&cat_id=1&story_id=229
The only reference to DadhiVāmana I could find, is in the sixth volume of Pratima Kōśā, which is a six-volume book on Hindu Iconography (pg.108-109), which further mentions the Meru-tantra, the Sāradā-tilaka and the Mantra-devatā-prakāśikā :
In the Pratima Kōśā, it is written:
Several forms of Vāmana are mentioned as for instance Dadhi-Vāmana (Meru-tantra 26, 341-342, and Sāradā-tilaka, 15, 56-60). In Tantra, he is derived from the conception of ‘dadhi’(curds) as the creative principle of life. In Meru-tantra Dadhi-Vāmana is visualised as seated upon a red lotus under the parasol of golden rays, lustrous like the full moon (’Jvalan Mayūkha Kanakaccatrādhah Puṇdarīka-gam) holding in his right hand a golden bowl filled with cooked rice mixed with curds (’Dadhyannam Vāma-hastena Svarṇasya-Cakśakam Dadhat).
Mantra-devatā-prakāśikā (cited in Prapanca-sāra-sāra-sangraha, Tanjore, Vol II, patala 31, pg. 904) which also mentions that Dadhi-Vāmana, makes him reside in the lunar orb (Candra-samstha) and hold in his two hands, a golden jar of pure water (Kanaka-kalaśam Śuddha-toyābhipūrṇam), and a golden bowl filled with cooked rice mixed in curds (’Dadhyannādhyam Kanaka-Cakśakam).