Financially things have changed a lot in the past year or two. Yes you're right to feel a bit upset about them removing their offer now you are under their roof. In some other circumstances I'd almost suggest they engineered it (girls having separate rooms for example, and then using that against a move to somewhere small).
Maybe they are thinking of a possible future where one goes into a care home and they don't want to lose their property to social services, so a family with school-age children living there would limit moves to evict one...
No, forget that suggestion!
Situation as far as mortgages is that you'd now need a massive deposit and then there's the risk of mortgage rates zooming up - and you'd have child care to consider on top, if you weren't really close to family.
I remember first getting a mortgage and having over 50% of my income swallowed up, and rates went up from 10% to around 14% (20 years ago, don't remember the actual figures but everyone felt it, and mortgage protection insurance came to the rescue when I lost my job, like many others - situation rotten even in IT 20 years ago wrt new jobs).
Not sure if you are even reading now, but while your immediate dreams were sparked by the offer from your parents, and your youngsters have it in the back of their minds about moving to somewhere of your own, it's got to go on hold for now.
Am not a great example (have been made bankrupt, and only have a roof over my head by chance, though 3 rooms have rain coming in) but seems like you need to give up some of the dream for now and perhaps go back into education so you can get a better paid job... perhaps after some other name change you can explore options for education / training and a brighter job prospect... and then some mortgage opportunities could be possible.
I know you've felt terribly upset, and hate being the 'youngster' whose views can be dismissed, but try to stick with it for 3-4 years and see how things change - if mortgage interest goes through the roof, you will honestly be glad you are still with your parents, while a proper career with financial independence has to be your aim so you can then be ready to move out, before your DC become teenagers and need to move schools.
Hard it will be, upset you may be, but you have had some turbulent times and try to see this is as a bit of calm before a storm ('teenagers' - even the word is dreaded by some!!) - anyway, good luck with all you do... never know, you might see a job that suits on MN in a year or two, for someone with sufficient IT skills to use a keyboard and mouse, and able to talk clearly... up for it?