I don't know if this is a reach but hear me out... Both her and Melanie seem to have a drinking problem of sorts, and it makes me wonder if they got that from their mam? They never really mention what the problem with the mam is but the fact she didn't show up at her daughter's wedding and they both alluded to the fact that she wouldn't even be at Jess' wedding if she was to have one, I wonder if it's a family thing and they don't want her at the wedding because of potential problems with alcohol?
I'm thinking this may be why Melanie is insisting on being sober, maybe she behaves the way her mam does and she doesn't want to be like her mam considering their relationship seems non existent? I don't know though, I am speculating. Either way, Jess clearly needs help, this is not ok!!