I've been a dickhead. How can I fix?

I have lost both my parents in the past 3 years.
I have been neither cruel or insensitive to anyone, strangers or friends. It has in fact given me insight to be understanding of any human.

Olivia sounds like a dick, and from your updates it sounds like she's always been a bit of a dick.

So Sarah's the nicest person in the world and she probably had to sit there and hear someone she hardly knows slagging her kids off?

Olivia's a bitch. I wouldn't want to be friends with her.

My husband died. I have managed at all social events not to say rude or mean things to others. As @PointWriter said you can't use grief as an excuse.

Grief doesn't make you into a cruel person, it doesn't change your personality.

It sounds like Olivia has a nasty streak and I'd distance myself from you, too.

Poor Sarah, that must have been horrible for her to experience.

I think with the update that the remarks were about Sarah's child that does put a different spin on things.
You can try a direct apology (but could also end up in a deeper hole if it turns out she didn't hear but has broken her phone/been on hospital with a relative/had a sudden urge to disappear off to a technology-free yoga retreat).
However if she heard, even if you apologise, chances are the friendship derailed anyway.

She sounds worse with every post!
I'd be taking a big step away from Olivia and spending my time with Sarah and other, kinder friends. Her nastiness and negativity isn't doing you any favours with making other friends. I'm sure you don't want to be tarnished with the same "mean girls" brush.

She'll be furious at being told she can't be a bullying bitch about people, especially a child? Why on earth are you friends with her?

Sarah,
I am so sorry that I didn't stick up for you the other day. I was a dickhead and a coward. I disagree with everything Olivia said but I was being too nice and feeling so sorry about her dad.
With hindsight I should have spoken about this and told her how wrong she was and how angry I was with her, rather than taking the coward's way out.
I apologise and I really value our friendship. I have been an idiot and it won't happen again (not least because I have put distance between me and Olivia).
If you want to get in touch I am here, but I do understand I have let you down.

Oh and to add, don't think she hasn't talked about you like this as well. You say she has form prior to depression -I'd put money on her talking shit behind your back too.

Well, no, not really. Grief isn't an excuse to be an absolute arsehole about someone's child (!) and their appearance. I can understand depression and being grumpy and out of sorts. I've suffered severe depression and had a nervous breakdown so I do understand how it can feel. It's still OK to tell her to pack it in though, being sad doesn't give you carte blanche to behave any way you choose and hurt other people.

Olivia sounds like a nasty piece of work that I would not be friends with.

She was a bitch about a child?! Fucking foul. And no her Dad passing doesn't get a look in.
Are you really the 'Olivia'?

I agree with this.
I also don't see how grief over her fathers death excuses your friend Olivia's behaviour in any way at all . Many many people deal with grief and manage not to use it as an excuse to hurt other people's feelings.
Edited as I've just seen your update. So it would seem Olivia is just an unpleasant person if she has been nasty all through her father's illness. Wanting other people to be miserable because things aren't going right for her.

I’ve been in a similar position to Sarah. Worst example was being over my paternal grandparents’ house and hearing my father’s new partner slagging me off behind my back as I returned from the toilet and they agreed with her! They were moaning about how fussy I was with food, which was a load of bollocks. I was more into Italian and Indian food, which they didn’t like. A big reason for this being I’m vegetarian and the veggie options are nicer! This nasty piece of work had only been with my father for a year and known me for a few months. I didn’t say anything but on reflection I wished I had.

How many days have passed since the party? If it were me I’d only bite the bullet and confront the situation as others have suggested If it’s getting on for a week since. People sometimes go off the radar unexpectedly for a few days. I’ve been known to inadvertently not reply to WhatsApp messages because I’d not seen them for a week.

How old are you? This all sounds very ‘Mean Girls’.

How are you people pleasing here? Sarah's not being pleased? Just Olivia the bully!

No advice here but I feel very sad for Sarah.
No way would I give a Person as mean as Olivia, the time of day!

I do understand, you obviously are not a bad person. I'd just be really hurt and the trust would be massively dented. You haven't had her back and she was in a situation with new people.
Hopefully you can clear everything up.

I wouldn't be too proactive and assume she heard. Maybe she just doesn't want to hang around with someone who has friends like Oliva, maybe her phone has died, maybe she's ill or some major thing has happened in her family.

If she didn't hear and you apologise for your mate bitching about her then that would be awful.

Be honest with Sarah and tell her you feel awful and you know you’re a dickhead.

Yes, I would bring it up. Tell her you were silent because of her dad’s death and that you’re sorry.

What did Olivia actually say?