Ug, she sounds like an awful manager. She has failed to tell you precisely what’s needed. Perhaps she expected you to know. On the other hand, things like knowing password, opening docs — come on, this is SO minor. You made the mistake once, you won’t again. Google Drive etc, she needs to pay for the course for you (an hour is not long!). You feel wrong footed/unconfident because you’ve been out of the work place. And while it may be irritating to your manager that you’re a bit slower, she could be a WHOLE lot better! Plus, it’s hardly like it’s a well paid job. It sounds entry level. So it’s unlikely others will be any more skilled than you. I once had this, aged 30, when I worked with someone who had expectations of skills I didn’t have (& never claimed to have). It’s incredibly demoralising. The difference was I was young(ish) and fully in work force so I didn’t have that extra layer of fear that comes from having been out of work for a while. Keep doing your job, op, get better at it day by day. Look out for something else, too. Your manager will quite likely always be a pain.
Btw how to persuade her: keep positive (hard when she’s undermining you), show willing, dress for the role (this sounds minor but it helps! Look smart or whatever the “uniform” is), go the extra mile where you can but not to detriment of your weekend/personal life (eg maybe ask if you can do courses in lunch break? Or do them yourself, independently, if that’s something you can do).
ps I wonder if she doesn’t have kids? If so, there can be a lack of understanding of what you are going through. In that case, do NOT talk about kids or family to her, keep it all very work focussed.