Are vegetables that grow underground disliked, and is it forbidden to cook several disliked things in one pot?

All that grows from the earth is permissible in principle, and it is not allowed to prohibit it or deem it disliked without a شرعي (Shar'i) — legally valid or religiously lawful — proof. There is no proof for disliking what grows underground, such as the vegetables you mentioned. And what the woman mentioned, that cooking disliked things together transforms them into haram, is a baseless statement. Cooking permissible vegetables together does not make them haram, unless the outcome is intoxicating, poisonous, or the cooked item itself is forbidden.