Hi lienelruot
Some good suggestions from others.
On another tack, if your wife manages to get her trousers down, at least sometimes, maybe try no knickers, so that there aren't 2 layers to deal with (I appreciate she may not find this acceptable).
You say she gets angry if you try to help (which is pretty understandable, she won't realise she needs help). Are you asking if she wants help, and she refuses - or could you just step in, in a matter of fact way, so she is helped before she knows it? Will she accept you in the bathroom with her, so that you could mime for her what she has to do, as an example? Maybe you could talk her through the process - I do this with dad, giving lots of praise when he gets each bit right - it feels odd to be telling another adult what to do, I know; but we'd not think twice about helping out a toddler (not the same exactly, I appreciate).
If you can accustom her to letting you help her, it'll make life easier for you both in the future as she needs more help with personal care - a lot easier said than done, I guess. I did find, with dad, that if I just did something as though it were an everyday occurrence, he went along with it, and neither of us were embarrassed. I sometimes even have to tell him to pee, as he's not sure what he's in the bathroom for. I appreciate it may not be the same with a spouse.
Maybe she can't quite see the toilet, especially if you have a largely white bathroom - some care homes have a brightly coloured toilet seat to make it stand out. Is she having trouble with the sitting down - maybe some grab rails would give her confidence.
Sorry to waffle on - ignore if not on the right track.
Best wishes