You don't actually know, unless they make you privy to their financial arrangements, that they also have cash in the bank to loan you that kind of money on a whim: my parents also look wealthy on the outside, with a house on the market at several million etc - but they have very, very little in the way of liquid assets (and not much more in assets, come to that), and most certainly wouldn't be able to loan me £1300 just like that.
Your car would have depreciated over 2 years, so may no longer have been worth anything like £4500, but presumably your father could only sell it as it was in his name? Or did he, like my mother (twice...) forge your signature to sell it? If it was still in his name, why? Was he still paying the insurance? Was it registered to you at their home, instead of theirs?
And you telling your mother you only have £50 to last two weeks when you have a small child and have chosen to study further smacks of wanting to be offered money: fair enough, but she probably is of the opinion that you've made your choices, and you must take the consequences- you did architecture and the car thing happened five years ago. Now you have a small child, and have chosen to do a Master's degree in a different area completely, within five years maximum of graduation - that's all well and good, but it comes with limitations, as you're finding out.
I don't know why your parents weren't more financially supportive, but YABU if you think they are suddenly going to change now. YANBU to wish it was different - and they were different: but they aren't. If you're struggling, ask directly instead of hinting - and see what response they come back with. What was their excuse when you asked them to help you at university, and explained that SF is predicated on parental support?
FWIW I'd be bloody cross if my daughter below £1300 on a weekend, and even if it was possible, I'd be crabby about lending them the money, as it would imply I hadn't managed to teach her - or she hadn't learned - the value of money at all.