Tolkien used a number of similar forms for “mother” for most of his life. The earliest of these are ᴱQ. amis (amits-) “mother” in the Qenya Lexicon of the 1910s along with variants ᴱQ. ambi, âmi, amaimi under the root ᴱ√AMA (QL/30). An additional variant ammi appeared in the Poetic and Mythological Words of Eldarissa (PME/30). In Early Qenya Word-lists of the 1920s Tolkien had ᴱQ. ambe or mambe “mother” (PE16/135). This became ᴹQ. amil “mother” in The Etymologies under the root ᴹ√AM “mother” (Ety/AM¹).
This 1930s form amil appears to have survived for some time. It appeared in a longer form Amille in Quenya Prayers of the 1950s (VT43/26; VT44/12, 18), and as an element in the term amilessi “mother-names” in a late essay on Elvish naming (MR/217). In the initial drafts of Elvish Hands, Fingers and Numerals from the late 1960s Tolkien used the form amilye or amye as an affectionate word for “mother”, and amaltil as the finger name for the second finger (VT47/26-27 note #34 and #35).
However, in those documents Tolkien seems to have revised the root for “mother” from √AM to √EM and the affectionate forms from amye to emya or emme (VT47/10; VT48/6, 19). The revised word for “mother” appears to be emil based on the 1st person possessive form emil(inya) (VT47/26).
Neo-Quenya: For purposes of Neo-Quenya, I prefer to retain the root √AM for “mother”, since that is what Tolkien used for 50 years, and ignore the very late change to √EM. As such, I would recommend amil(le) for “mother” and affectionate forms amme “mommy” and amya. However, if you prefer to use Tolkien’s “final” forms, then emil(le), emme and emya seem to be what Tolkien adopted in the late 1960s.