Complete the sentence.
My _______ has many tips on finding deals at the grocery store.

"sister, a single mother of two," is correct. The information inside of the commas is nonessential to the meaning of the sentence. It is simply extra information for the reader.
"sister: a single mother of two" is incorrect because a colon is used to elaborate, but the rest of the sentence is essential information and does not make sense as a simple elaboration.
"sister. A single mother of two," is incorrect because the way the period separates this into two sentences does not make sense grammatically as it is incomplete.
"sister a single mother of two" is incorrect because it causes a run-on sentence and is grammatically incorrect.