Thanks for the responses. I can understand now why she thinks I have gone over her head and it has put her nose out of joint. I'll think again in the future if this sort of thing comes up again.
It wasn't exactly my intention to go over her head, I just wanted to get things sorted and my boss wasn't around so I asked her boss. It wasn't an outlandish request so I didn't see a problem.
My problem now is that even though I am perfectly entitled to work from home on this occasion - it's not something to be done all the time but we are allowed if car issues, bad weather, needing to wait for a delivery man etc - and the top boss has said yes, no problem just let my line manager know, however I feel like I'm taking liberties and somehow being lazy by not coming into work while my car is in the shop all day and I should go to work after all. Of course, I have no way of getting there so I can't, but this makes it worse. This is because my boss was so snippy and suggesting that my car didn't need fixing that badly, that the garage should drive me to work, it wasn't a proper garage if they wouldn't do that.....all kinds of reasons why she was making it sound like I was lying or something.
Even though I've explained what I'll be working on, I think it's because my boss was obviously doubtful that it should be allowed, and largely because she doesn't trust anyone to work unmonitored. Last time I worked from home was the snow day a year ago and she called me on the hour every hour to ask me pointless questions, just to check I was working, even though I was copying her in on emails as it was concerning a project she wanted to be kept up to date on. She did the same to my colleague. She wasted more of our time doing that actually, than getting work done.
Colleagues on my grade, and some lower, don't have these issues with their line managers. She knows the policy is there, but she somehow thinks it's all at her discretion and I don't see a way around that.