Adult relatives, partners, acquaintances and colleagues can all be dealt with in the same way. Politely but firmly and with no room for messing about. You don't depend on any of them to pay your bills, so you don't have to accept any level of rudeness from them (unlike if your job was dealing with the general public for instance).
I've spent 20 years working in a field where it's necessary for me to occasionally regularly be very firm and to make it very clear that I won't tolerate any nonsense, all the while being polite.
Do you have a look? I mean the sort of look a stern old lady would give you, looking at you over the top of her glasses? Channel your inner Miss Marple. I know it sounds mad, but I have one (including one eyebrow raised) and if I ever use it, the person I'm looking at is left in no doubt that they've over stepped the mark. Coupled with maintained eye contact and a firm, confident 'I beg your pardon?' it works wonders. Also, use the broken record technique. If someone is trying to manipulate you into doing something you don't want to do, say no. Repeatedly. Never make up an excuse or tell them that you'd do it if you could, or that you're really sorry you can't help them because that gives them an opening to try and change your mind. If you're not confident enough to refuse an explanation, tell them that it's just not going to work for you and repeat until it sinks in. If an acquaintance is being unpleasant and it's not out of character (everyone can have an off day) drop them. You owe them nothing, they aren't important enough to you to have established an actual friendship with them, why would you accept that from them?
I think that people who aren't used to challenging people on their rudeness can often find that people get very upset with them when they start because they aren't used to you standing up for yourself. Don't give up or you'll be in a worse position than before; still being treated badly but with no confidence to change things.
I think identifying when it's appropriate to put someone in their place and when it would be better to just smooth things over or remove yourself sharpish is a skill that you'll learn in time and with practice. It will come.