Babushka appears in Merriam Websters online, so it qualifies as a loan word.
I'm not sure using these reading cues will help readers in the targeted grade levels. Reading a word, even with phonetic help, does not ensure correct pronunciation. Even adults may struggle with it if they aren't very familiar with pronunciation keys. (I see this with Yiddish and Hebrew words). The visual cues can only take you so far. You need to hear it, or at least, I do. I think this is something I would leave for a conversation with an editor interested in publishing the story. Of course, if you are self-publishing, go ahead with it.