Thank you for the suggestions so far. Now I will share the ones I have been thinking of (long):
The Baxter parents from "Be Nice to Nancy!" aka "Be Nice to Nikki" (Judy and M&J respectively). Not only do these parents refuse to listen when Yvonne tries to tell them Nancy Norden is a nasty piece of work who is giving her life a misery but they are also unwitting parties to the bullying in the way they keep pushing Yvonne towards Nancy, which makes Yvonne open to Nancy's bullying in her own home as well as school. I think Mr Norden should also be mentioned as a bad parent for that idiotic suggestion that Yvonne be friends with his bully daughter in the first place. Did he seriously think it would change her ways? It doesn't say much for his own parenting skills or brains.
http://girlscomicsofyesterday.com/?s=Be+Nice+to+Nancy
Mr Rawlings from the Sandy trilogy (Tammy). A father who still treats his daughter like a little girl. Okay, so that's a common one. But he compounds the problem by having very narrow views on who should be Sandy's boyfriend, and his choices are guided more by his snobbish attitudes and business connections than Sandy's tastes or wishes. He doesn't listen when Sandy tells him she doesn't agree with his choices, saying she's too young to know her own mind (she's 13!). He is also a snob and political type who shows little empathy for others. For example, when he becomes education officer at Birchborough his first act is to close the schools to after-hour activities, just to save money. He does not care how this will affect people - including Sandy, who finds nobody wants to know her at Birchborough High because of it. In the end he loses that job, gets a long-overdue humbling, and Sandy finally gets a boyfriend both she and her father are happy with.
The Street parents from “Cora Can’t Lose” (Tammy)
https://jintycomic.wordpress.com/2017/0 ... lose-1984/
They put their daughter Cora down and bully her with nasty, sneering remarks because she is not winning sports trophies as they did. This sends Cora into a crazed drive to win as many trophies as she can, which makes her unpopular and even endangers her life.
Mrs Shaw from "Hard Times for Helen" (Judy)
http://girlscomicsofyesterday.com/2016/ ... n-1984-85/
Mrs Moore from "No Haven for Hayley" (Tammy)
https://jintycomic.wordpress.com/2017/0 ... yley-1981/
These two serials have been put together because they are similar in concept: a widowed mother who neglects her daughter, takes her for granted, and uses her as a dumping ground because she is too busy with charity work. The ways in which the mothers are too busy are a bit different. The former is a slave to duty and can't say no, has been lumbered with a charity job that is too demanding. The latter is a workaholic and often gets big ideas that are more stupid than realistic.
Mrs Noble from "The Goose Girl" (Jinty)
https://jintycomic.wordpress.com/2015/0 ... girl-1977/
Mrs Marshall from "The Four-Footed Friends" (Jinty)
https://jintycomic.wordpress.com/2014/0 ... ends-1979/
Again these two serials have been put together because they feature mothers who have reacted badly to grief and developed hangups that cause everyone around them to suffer, including their own daughters of course. With the former it is a pathological hatred of birds, stifling her daughter's talent for ornithology, and constantly pushing her into fashion design against her wishes. With the latter it is getting too overprotective of her daughter against germs and "common" people, and hating common people to the point of trying to drive them out of their new housing and into the slums they came from.
There was also a story in Suzy, the title of which I do not remember, where a mother reacts badly when her daughter Sheila dies of an illness contracted while swimming. She starts hating swimming, bans it in her household, and keep lashing out at her two remaining children. The remaining daughter, Jenny, is constantly picking up after her mother, who constantly leaves the place as a tip and doesn't pay the bills. Jenny starts secretly swimming for the championship her late sister was going for, on top of all her other work in picking up after Mum. No wonder she collapses from exhaustion in the final episode!
Mr Simons from "Daddy's Darling" (Jinty)
https://jintycomic.wordpress.com/2017/0 ... ling-1975/
Mr Simons loves his daughter Lee. The trouble is, his love is totally selfish and excludes all others, including friends Lee wants to make.
Mr Graves from "Dracula's Daughter" (Jinty).
https://jintycomic.wordpress.com/2014/0 ... hter-1981/
A fanatical grammar school disciplinarian who believes there is only one way to run schools - his way. When he becomes headmaster of Castlegate Comp he forces his views right down its throat, even going as far as butting in on classes and ordering teachers to run lessons the way he wants. His daughter Lydia is most embarrassed and it is causing a lot of problems for her, but Dad refuses to listen or slow down his drive.
The Grey parents from "The Black and White World of Shirley Grey" (Tammy).
https://jintycomic.wordpress.com/?s=shirley+grey
When you believe your daughter has been wrongly charged with a crime, you are totally supportive and worried about what is going to happen to her, right? Well, not these parents. They treat her harshly and don't lend any support or sympathy at all. All Mum cares about is herself and "the shame of it all", and Dad isn't much better.
Sir Edgar Whitland from "The Fairground of Fear" (Tammy).
https://jintycomic.wordpress.com/2018/0 ... fear-1976/
Purportedly Julie Whitland's adoptive father (actually her grandfather). A super-snob who stifles Julie's life and who she mixes with because he doesn't want Whitlands mixing with common types. At first Julie thinks his bigoted, snobby attitude is just misguided - but then she finds out the real reason for it and the monster he truly is!
Now for my number 2 "worst":
The Harvey parents from "Waves of Fear" (Jinty).
https://jintycomic.wordpress.com/2014/0 ... fear-1979/
This must rank as the worst emotional reaction from parents in girls' comics in history. These hitherto loving parents turn into the worst pair of ogres I have ever seen in girls' comics.
Now, you're probably wondering: What is my number 1 "worst"? Okay, drumroll please...
The Petty parents from "Bad Luck Barbara" (Mandy)
http://girlscomicsofyesterday.com/2016/ ... itch-1991/
Not only do these parents constantly let their daughter Barbara down when she tries to tell them the villagers of Wavertree are harassing her because they think she's a witch but they never find out their mistake and learn from it either. The problem just doesn't sink in, even when it is staring at them in the face. When Barbara tries to tell them, they just laugh at it, belittle it, tell her she's being too sensitive, the villagers are just teasing her, etc, etc. Above all, they tell her they can't leave because of Dad's job, so stop it, the job means a lot to him. It sounds like they are putting Dad's job before their daughter's welfare - or even her life!