Sicilian is NOT a dialect of Italian. That's a very common misconception. It is a Romance language (Latin-evolved), just like Italian, French, Spanish, Portuguese, Romanian, Catalan, etc. It is a sister language.
It is far more than learning different vocabulary. It has a number of sounds that set it apart from Italian and other Romance languages (they are not unique sounds, but are uncommon among Romance languages).
It has different grammar as well.
It's another language.
Your mother does not speak Italian. She speaks Sicilian. Learning Italian certainly will help with learning Sicilian, but you're not learning Sicilian. They are not dialects of the same language.
It is not like speaking American English versus British language, which are dialects of the same language.