WOW 100% say YANBU. Never seen that before.
@Boredhimtodeath You need to be really strong and firm here! Youe cousin is taking the piss. How DARE your uncle ask you to wait for her/change your hours for her. What a cheek. And as for the 'it will cause discord in the family if I don't do it' comments. Ewwwwww... I feel ya!!!
It reminds me so much of my extended family, and is one of the reasons I moved away (40 miles) from where I grew up. I was berated and scolded if I didn't jump through hoops for certain family members, just because I was the second youngest of 10 cousins. My brother was the youngest. But like the rest of the 'males' in the family, he was never expected to do anything.
Some of the family was so obnoxious and bossy, and assumed that the younger females should do stuff (for free) for people..... and bend over backwards, even if it was massively inconvenient for them...
Like give lifts, give money, give items away for free, run errands etc. My aunt once expected my DH to help my cousin and her new boyfriend to move house, (and book the day off work to do it,) and another auntie expected me to give another cousin our old TV when we got a new one. (Hers was 15 years old and was beginning to pack up...)
We said the kids were having it for the conservatory, but she frowned and tutted and said 'CHILDREN don't need to have a spare TV, and Sharon can't afford a TV, she is broke.' I thought 'yeah, soooo broke ... but she - and her DP - can afford to smoke 40 cigarettes a day between them, and spend £25 to £30 in one night (two or three nights a week) on Bingo, or at the pub! I said no and got slated for weeks for being 'unkind.' 
When my parents passed, I moved away. I have fuckall to do with any of them now; just my brother and his wife and kids, and 2 aunts and 3 cousins who moved away from the rest of the family in the 1990s.
Urgh, families can be so toxic!