1 is correct while quite off with 2
했어요 vs 하고 있었어요:
You focus on that/what she cooked, and that you will eat what she cooked as next
You focus on what she was busy with. I'd translate it to "my mother was busy cooking"
2 is incorrect because:
~하면서 ~하다, both activities shall refer to the same subject, emphasizng the subject doing both simultaneously.
v1 is correct, while v2 suffers the same problem: subject sharing.