I) Your first question Did Śrī Rāma's three brothers viz. Bharata, Lakṣmaṇa & Śatrughna too, pledged with the 'Eka-patnī-vrata'?
Except Śrī Rāma, the sankalpa of Eka-patnī-vrata for other brothers was mentioned no where.
II) Your second and final question If not, what's the story/information on the 'other-spouses' of the other three brothers?
King Dasharatha(दशरथ) who ruled Kosala kingdom had four sons and here is the spouse details of his sons:
Rāma married Sītā(सीता) who was the daughter of King Janaka of Mithila.
Bharatha married Māṇḍavī(माण्डवी) who was a princess of Videha.
Lakshmana married Urmilā(ऊर्मिला) who was born as the daughter of
King Janaka and Queen Sunayana of Mithila and younger sister of Sīta.
Shatrughna married Srutakīrti(श्रुतकीर्ति) who was a princess of
Videha and younger sister of Māṇḍavī.
Beware-1: Kushadhvaja(कुशध्वजा) was the King of Samkasya and the younger brother of Janaka the King of Mithila, was married to Chandrabhāgā(चंद्रभागा) and was the father of Māṇḍavī and Srutakīrti.
Beware-2: There was no mention of the other spouses of other brothers of Sri Rāma.