おねいちゃん is just a misspelling of おねえちゃん. This word probably contains lengthened vowel from ane: ane → nē, so there is no rationale for ei in this word. (Compare the same process for ani → nī.)
A part of Japanese population pronounces ei within single morpheme as [e̞ː] instead of [e̞i]. There are much more words with originally ei than ee / ē, so some persons, by analogy, may use ei spelling even in cases where it is not legitimate.
Regarding words with correct ei spelling, pronunciation as [e̞i] or [e̞ː] may depend on dialect, and also pronunciation as [e̞i] is more likely in formal or careful speech.
Words with morpheme boundary in the middle of ei (e.g. 眼{め}医{い}者{しゃ} "oculist", 姪{めい} "niece" (this me is the same morpheme as in words 女{め}, 雌{めす}, 女{め}神{がみ}, 女{め}子{こ}, 娘{むすめ}, 嫁{よめ}, 姫{ひめ} etc.)) should have both vowels pronounced distinctly: [e̞i].