Thanks for the explanation - will definitely see if I can get more data on our family's origins.
Very interesting take... I would agree with your Hebrew phonetic spelling of her name - while I haven't seen any documents with her name written out, ציזינו is definitely the correct phonetic spelling in Hebrew.
Which makes anything about ציצינו irrelevant.
It is pretty clear to me that ציזינו is a diminutive or endearing form of ציזא or ציזיא. IINM the Rachmestrivker had some great grandmother named חנה ציזא or חוה ציזא. Maybe you can try that angle to try and find out the etymology. Otherwise I would look to someone with Slavic language/names expertise to try and figure it out.
Also, what what her English name. Sometimes those were given to resemble sound, and sometimes actually had a connotation to the meaning.