She was rude and overbearing, but with the benefit of hindsight I think you could have handled things better, OP. I suspect she thought you were trying to be over-involved following your text to her of the funeral details and that set the tone for her whole attitude towards you. I really don't think you should have pushed the conversation with her, and certainly not commented on her rudeness in that setting - it was about the bereaved family and you ran a real risk of distracting from that, but I can see how it happened.
You just need to let it go. No need to glare at her. No need to do anything. It happened in the context of something much, much worse - the funeral of a no doubt much-missed wife and mother - I think you need ot put it behind you. Any continuation or escalation will make you look very bad.
Funerals often trigger some very odd behaviour. "Competitive grieving" is definitely a good way to put it. A friend of mine from uni moved to my home town, joined the same sports club as me and finished up house-sharing with an ex with whom I was still good friends. A couple of years later he died very suddenly and unexpectedly of an undiagnosed illness. By this time I had moved away but was still in touch with people back home as my family still lived there. My ex, who was helping with a lot of the organisation, called me to let me know, and, at the request of our friend's parents, asked me to pass on the news and the funeral details to some other people from uni I was still in touch with - it is a fairly small sporting community with all sorts of overlapping social circles.
I went home that weekend and found a whole group of people barely speaking to each other as two other friends who were usually lovely, had appointed themselves "mourners in chief" and were effectively trying to take on the role of monitoring access to the funeral. My ex was incredibly upset and admitted afterwards that he found them completely smothering, but it was easier just to let them get on with it. They were intercepting people and telling them that my ex was too upset to discuss funeral details, and that the funeral was for family and close friends only. When I spoke to them I got the same spiel and I didn't bother telling them that I was going with another group of people in any event.
In the end they and my ex were the only people from my home town to go to the funeral which was a couple of hundred miles away. I travelled separately with a group of old uni friends. When we got there, the two friends reacted incredibly badly - there was lots of glaring and muttering, and eventually one of them came over to me and said in a hushed voice that she thought it was going to be a bit awkward with me being there as it was close family and friends only. Before I could say anything, one of the deceased's best friends and coffin bearers came over and thanked me for doing all the ringing around as the parents were keen for as many people as possible to be able to attend. The two overbearing friends seemed genuinely put out and were quite unpleasant for the rest of the funeral and reception and weren't ever particularly nice to me again.
All that I appeared to have done wrong was to be part of a different social group who were given the correct information about the funeral, thereby bypassing their self-appointed "gatekeeper" role. They weren't particularly good friends of the friend who died - they just seemed to want to cast themselves in a central role. I could have said something to them - I didn't. I just didn't bother with them again.
Emotions run high at times like this - best just to accept that your former friend isn't quite the person you thought she was and avoid making this any worse than it needs to be.