Speaking as someone who has become estranged from a previously I thought very close family member, i am aware that resentments can build up over time - (as this one has) and by the time it gets to the stage of either party asking for (or expecting) an apology - the risk of falling out permanently is definitely there. I don't think you would want to be in that situation.
With this in mind, and with the greatest of respect I would like to ask you to try to get some perspective.
You have both been stressed for various reasons. You, because you are finding the commitment you took on, in fact too much. You also sound as if you are frightened of losing your daughter. Which is understandable.
In fact, you are allowed to say how much you can take on. That's reasonable. If you haven't managed to do this though, and express your needs or limitations, then it is perfectly possible the other person has not noticed how stretched you have been. No blame attached to that on my part at all, just that none of us are mind readers are we?
Your daughter has been stressed because she probably feels she has failed as a mother - and is feeling resentful herself. And angry because you were cross with her kids. Or she thinks you were. I'm not sure how bad it was. If you had said something like 'oh for goodness sake, I wish your mum would remember to put a sweatshirt in the bag'...I don't think that would be that bad.
Regardless, it is very clear you are a caring grandma, and to be frank, not a child abuser or a serial killer. (Just to use exaggeration).
You haven't broken the law, neither have you harmed her kids beyond repair.
On the scale of it, what has actually happened? The kids are safe. Fed. Warm. Loved. Aren't they?
You and your daughter's family are safe. Fed. Warm and both holding down full time jobs. In this age of Covid actually an incredible achievement.
It really can be stalemate in a relationship when both of you are expecting an apology. And neither can truthfully give one for their own reasons.
I think in this situation I would get a bit of distance. Definitely ask someone else to look after the cats. Don't think either of you need another situation where things might go wrong. For example if your daughter couldn't feed the cats one day - which might lead you to think she did it on purpose.
You don't need to get into that situation again. It's not going to do your relationship any good.
I have noticed recently that especially with kids, all kinds of things can be misunderstood and misinterpreted, and lets face it as adults we carry round our own baggage from the past, anyway.
This sounds like a very tricky situation and I don't envy you.
Hope you can iron it out.
I feel a big part of the solution is to reassess your own needs, look after yourself, make clear that certain things are too much.
Wouldn't like to offer an opinion on apologies. Aside from personally I would rather do without the actual words, and see the person reflecting and doing things differently in future.
I think some people get into helping, and then attach their own agenda to 'helping' which creates a kind of dependence or even co-dependency which personally I don't wish to be a part of.
It's always the dynamic that bothers me more than what actually happened.
I'm a very practical person though, and certain that I would be perceived by some people as insensitive for that reason.
People talk about languages of 'love' and that's mine.
I personally feel that insisting on the words - 'I'm sorry for x' gets in the way often.
In misunderstandings with my own daugther and tough times, it goes a long way to say 'I love you'
Totally cheesy I know but as in the film,
'Love means never having to say 'I'm sorry'
Whether you agree with that or not, I feel sometimes people demand the words, and forget the emotion. And if the emotion is not right, then it somehow renders the words meaningless.
Sounds like you love your daughter and are maybe really conscientious and afraid of failing her.
Perhaps she feels the same? Good luck