You can't just split on comma. To implement a proper parser for that case, you need to loop through the string yourself, keeping track of whether you are inside quotes or not. If you are inside a quoted string, you should keep on until you find another quote.
IEnumerable LineSplitter(string line)
{
int fieldStart = 0;
for(int i = 0; i < line.Length; i++)
{
if(line[i] == ',')
{
yield return line.SubString(fieldStart, i - fieldStart);
fieldStart = i + 1;
}
if(line[i] == '"')
for(i++; line[i] != '"'; i++) {}
}
}