Re: 1)My mom has been working ever since I can remember. 2) My mom has been working ever since I could remember.
Sentence 1 is correct. Sentence 2 has the implication that you are unable to remember anything at the present moment and have to rely on the/a time that you COULD remember.
"Since" refers back to a specific time. "For as long as" refers to a continuing period starting at a specific time and continuing to the present. Because remembering is a continous process, it is more natural to say "has been working for as long as I can remember." You could, however, say "has been working ever since she left school/left home/came to this country, etc." -- that is, ever since
You cannot use "could".The act of remembering takes place in the present. If it is past tense, then it implies something has been forgotten. "Since" means the action has taken place from the past to the present. "I've lived in Taipei since I was born."