"My maternal grandmother and I."
Translation:Shi dóó shimasaní.
You're trying to apply English rules to another language. If you do that to every foreign language you learn, you will always make mistakes learning them. Rules that apply in English don't necessarily apply to other languages. Yes, in English the order "my mom and I" is correct, but this is not how Navajo orders it. They order the Subject "I" first and Object "my maternal grandmother" and then the Verb, if present.
In English, it's grammatically incorrect to say "Me and my grandma" , you're supposed to say "My grandma and I". In Navajo the sentence just flows better when it's "Shi doo shimasani". Since, "shi" can mean "I/me/my/mine", placing it at the beginning of the sentence when you're not referring to owning/describing anything reduces subject/pronoun ambiguity.