I have been looking at different Grade 2 lists on the web. I see some lists that have this:
1 引 Pull イン ひ（く）
as the first character in the list for Grade 2 and other lists have an assortment of different characters.
Is there some place an official order for Kanji within the grades or even an order that covers all the kanji starting with the first kanji or Grade 1?
There is not a determined order of how students learn kanji within each grade. For example, Japanese Ministry of Education determines the first 80 kanji that first graders must learn, but different textbooks teach these 80 kanji in different orders, using different reading materials.
引 is listed as the first kanji among the 160 kanji for the second graders, but this is simply because it's the first character in the alphabetical (i.e., あいうえお order) order of on'yomi.
The kanji lists by (elementary school) grade are called 学年別漢字配当表【がくねんべつかんじはいとうひょう】*.
* It's totally irrelevant but all of the kanji are learned by the third grade.
The official chart is sorted by kana ordering in on'yomi, then stroke count, then radical. The sorting is, however, only for the indexing purpose and does NOT have any meaning as priority or teaching order, except the grade number. Therefore the "official order" is not existent.
