Teens don't always behave better when faced with illness in the family, initially they may behave worse! I think over time they will process this, and may eventually turn out to be quite considerate and helpful, but teens, even adult children, don't like it when the social order of the house is disrupted and they may end up acting out or storming out, just when you would like them to be the best version of themselves. I would do two things, one is get them some adult support from outside the home, whether through a local cancer charity, school counselling and so on. The second is, I'd call it as I see it if they are being obnoxious- don't guilt them and say 'your dad's got cancer' because that won't help, but it's fine to say- you know what, you are being provoking and I have other things on my mind, no I won't give you a lift if you are being a twat.
It will take a while for everything to bed down, and it will be disturbing and upsetting for them even if they don't say that out loud.
I would also try to get some support for yourself, as the one left dealing with everyone else, so therapy, cancer support, good friends, so you have a place to offload, and calm yourself (meditation, mindfulness, venting) rather than shouting at them.
My children have had to deal with this, and sometimes they've been kind beyond belief and other times they've been awful. They don't stop being teens because bad things are happening in the family unfortunately, but over time they can learn to rein it in and may even offer help/caring, although I've found that happened with later ages rather than 14/16.