I would suggest that you make contact with Latvia Archives before your trip. There are phone numbers you can call and speak in English. Don't quit on Raduraksti -- you have specific dates. Your missing ingredient is name of church.
I respond to some of your many background findings. I would not pursue Schmerli Cemetery. It is on outskirts of Riga. Rozental is not a rare name. It is common to Latvians, Germans and to Jews. While not an exclusive Jewish cemetery there were many Jews buried there. It is likely that Janis Rozental was buried in a Riga cemetery, perhaps one closest to where lived. I cannot now locate the history of Natalijas Draudzinas gimnazija but have seen it in the past. My recollection is that its location has changed three times. I think that when your mother attended it waqs not at the current location and maybe was an all-girls school. MOAR on the photograph I believe was hand written and stands for MargaritaOzolsArvidRozental. Krecbergs I believe was imprinted on the photograph. It has to be photographer. His studio address can be found. I believe that the name is Kreicbergs. Last year a well known photographer by that name died at age 72 in Latvia. A relative of his I believe took the photgraph you have. I believe the Archives cannot help you with Soviet time records and Janis died in 1946.
The ina [with comma underneath the n] is common and indicates small or endearment form of the root. It also indicates feminine, masculine ending is ins [comma underneath n, check mark above s]. Closest to root mut is mute [mouth] and mate [mother]. It is the latter, maybe from dialect but I suspect from Mutter - German for mother.
I respond to other issues in another posting. Arturs Zageris