I'm sorry your father was so horrid. Probably not a huge surprise to you, but extremely hurtful all the same. Yes - you have children, and therefore, arguably, you're in more genuine need of help than someone who has no dependents and who's in the very fortunate position of embarking (so you say) on yet another career direction, courtesy of the bank of Mum & Dad. In any case ... you referred back to when the pair of you were children yourselves, and she was still favoured even then, so his current argument really doesn't hold water at all. It's very very mean and I don't know if you'll ever get to the bottom of it .... I despise parents who treat their children differently. Okay ... there are times when it is necessary to treat kids differently, but overall, it should be a swings and roundabouts situation, where no one child benefits more than the others (unless there are genuinely extenuating reasons such as one off emergencies, sudden serious illness etc).
I agree that in an ideal world, adult children should sort their own problems out. Just as, in an ideal world, parents should have had the foresight (and actual ability) to plan for a comfortable old age. But real life isn't always kind - regardless of how hard you work, how nice you are, or how much you try to make sensible plans and for me, the bottom line is that when someone who you should - in theory - care for, is in trouble, you do what you can to help them out. Works both ways. Obviously, with the best will in the world, not everyone can solve all their nearest and dearest's problems, though even being there with a sympathetic ear can go a long way. However, in this case, the OP's parents do appear to be in a very enviable position and are able to help her should they want to .... and that's the horrid reality, they don't seem to want to, and aren't prepared to explain why. That in itself would be hard to accept even if the OP had no siblings, or, if her sister was also treated in the same way - i.e. no financial help .... but the fact the sister is given (so the OP says) "huge" sums of money (and the only sum she's actually disclosed to us of £150k is pretty significant by most people's reckoning) must feel gutting. Sounds to me like the younger daughter is playing at life - flitting about from course to course with no real idea of what she wants to do - nor any real incentive to buckle down and sort herself out because she knows mummy and daddy will pay up when asked, thereby cushioning her from the real world.
Meanwhile, the OP's dad (offer of work - possibly on the cheap and less than fair going rate depending on what needs doing !!! (which is pretty disgusting) - notwithstanding) sees no hypocrisy or favouritism in paying his younger single daughter's living costs while she sets up a new venture (about which, presumably, there's no guarantee of success and potentially it could be money down the drain) whilst his older daughter and grandchildren are in danger of losing their home. The total and vast disparity between the two respective situations is gobsmacking and I feel so terribly sorry for the OP ... both for all her understandable and genuine worries, and for the fact her parents are so cold. All the arguments about adults standing on their own two feet, parents spending their money as they wish blah blah blah really don't apply when you have another perfectly able bodied adult child being treated totally differently. I couldn't live with myself if my child was in real danger of losing their home, or even struggling to buy food, while I had the sort of available money the OP's parents do. And I couldn't bear to insult my older child's intelligence by suggesting that their younger, single and childless, sibling was somehow in more "need" (as per the circumstances described).
I really hope your mum is more sympathetic OP.