Nagynéni and néni are the same?
In German Tante, aunt, néni is the sister of one of your parents. And Großtante, grand/greataunt, (nagynéni#) would be the sister of one of your grandparents. #But it seems we need a higher level in Hungarian "nagy nagynéni"?
Rather unnecesary complication to use the -ke/-ka forms when it is complicated enough.
Hungarian doesn't have terms for siblings of your grandparents (besides "nagyapám testvére" etc.). But the diminutive forms "nénike" and "bácsika" are barely a step beyond baby talk, used in my experience only by families with very young children; they are completely inappropriate to this context.