I'm going to ask my mother to not chew gum around me
Does gum chewing bother you that much?
I hate the wet sound it makes.
As long as you are asking your parent this question respectfully then you should be fine. Just be careful not to use a rude tone with this one. It is only natural to not be a fan of loud sounds when people eat.
I don't want to hear that wet mouth noise anymore.
You should find a better way to ask her to stop. Wet mouth noise sounds a little rude to say to a parent.