Op I can understand you're concerns, but honestly having been through similar with my dd I think it's very possible she will come around to a different way of thinking.
My dd left school at 16, tbf not totally get fault school were being arses about her disability and unsupportive. But her disability didn't prevent her working at this point (it may in the future)
She was living with me though as I said to her she wasn't just lazing about at home. She either went to college or got a full time (min 30 hours) job.
She got herself an apprenticeship in which she did really well after a shaky start.
When her friends starting leaving school and going uni a couple years later, this led to her re-evaluating her own situation. She also broke up with a long term boyfriend around the same time.
Her job was ok, good pay for a "kid" but not a career she really wanted.
So she went back into education, and she is now heading off to uni this year, a red brick no less.
I've also observed similar circumstances in other families and the parents get really stressed (as did I)
But in every case the "kids" have come good in the end.
One took until the son was 30 till he got his head on straight, he'd been drifting and then met his now wife, who is a lovely but quite blunt woman. When they met she made it very clear that she thought he was capable of more and was drifting and gave him both the confidence and the kick up the arse to do better. He'd started uni but dropped out before end of first year and thought it wasn't for him. She pointed out maybe it was more the uni/course wasn't for him, encouraged him to consider other options which he did and he's now in a career he loves and is doing really well, they're now married with 2 kids of their own.
Generally when they start encountering situations where they're missing out on nights out, concerts, holidays etc that their friends are all participating in, when they see those friends buying nice clothes/tech, then cars and houses they start to reassess themselves and understand they have to sort things.
But also, this particular past year has been horrific for teens/young adults. There are fuck all jobs about of any kind (when did you last job hunt op? When did you last do so when you didn't have any/relevant experience? I have a number of friends who've been made redundant or lost businesses due to COVID impact in the last year. These are people in their 30's/40's/50's with degrees - even advanced degrees - and tons of good work experience and references and they're really struggling to find work/enough work, the ones that have found work all but one has only found part time/zero hours so far) education has been hard hit and a lot of youngsters have made the decision to wait a year or two until things settle, my own dd debated doing this too. She is hoping things will be closer to normal by Sep/Oct.
She's been in tears at points with how hard it is to really engage with education remotely, to study online etc.
I'm so proud of how well she's done even more than if she'd been doing this in "normal" times because it's been damn hard for them! A number of people dropped out of her course because they simply couldn't cope under the current situation.
Give her a bit of a break, keep communication channels open so that you CAN influence her properly and counteract the lack of motivation from her father. (I can relate to that too but would prefer to keep it in pm if you're up to that)
Can she drive yet? I'm guessing when it gets to the point all her friends can drive and have cars she'll be wanting the same - can't do that on a part time job and uc.
Plus, as others have said uc "discipline" has been less so this past year.
I actually have a few in my circle who work for dwp and they are totally overwhelmed between 100,000's more claiming and constant regs changes and they're working crazy hours too.
When things calm a little I suspect it'll be "business as usual" which will mean 2 major changes
Loss of COVID bumps in money
More pressure back on to get people off uc wherever possible and an 18 year old fit to work with no caring responsibilities will likely be under a lot of pressure to find and keep a full time job or be at risk of sanctions.
Regarding potential fraud - does she have a different surname to her dad? Is he on birth certificate?