It's hard to say without knowing what her 'needs' may be, but if they're beyond simply being a friendly face and some company I'd have no issue in saying no immediately. It's a lot of responsibility, especially with the added pressures of no sleep, changing planes etc.
If it's just company she's after, then it's harder to say no and I'd have a real dilemma because every part of me would want to say no (but I can be a real mug and would then end up resenting her for the entire journey, then feel even worse about that!).
I adore travelling on my own - regardless of everything that goes on at an airport and on a plane, it really can feel like I'm actually getting some peace and time to myself.
I love getting to the airport in good time and spending the wait mooching around the shops, going for a glass of Champagne and topping up my make-up bag. Then on flights I have absolutely no interest in speaking to anyone, I just want to watch movies, read crap, maybe doze if I can. Even when DH and I travel together, once we've gone through security we tend to just do our own thing, meet again to board then just do our own thing again on the plane (next to each other!). Bliss!
OP, if you've been looking forward to this trip and wanted to spend the time at the airport and on the flight doing what you want, when you want, then say no and don't feel bad. It's not your responsibility and your friend needs to arrange assisted travel for her mum.