As someone who has been in a similar situation with a friend group, and myself being the one that (IMO) was wronged by another friend in our group, it changed the dynamic of the group completely. The ‘friend’ narrated her side of the story to the rest of the group early on, (supposedly) was so upset and got the others to feel sorry for her, they rallied round her, whilst I was left to deal with things on my own, as I didn’t go running to them as didn’t want them to be caught in the middle so tried to leave them out of it. So I wouldn’t take friend 1’s lack of being upset as meaning she isn’t as bothered, maybe she’s just being more adult about the situation and trying to not make you all feel awkward.
The ‘friend’ and I were past the point of making up, even though the others in the group tried to encourage me to make up for the ‘good of the group’. And that was my choice which I accepted, but it didn’t mean I wanted to not be friends with the others.
They essentially picked sides by inviting her to things and not me, and the groups reason for this was that they were doing things as couples and as I was single, but she was married, so was hard as their husbands were friends too.
I very rarely got an invite out at all, and felt like they had sided with her, so by the time I did get the odd invite, I felt like they weren’t real friends and so took myself out of the situation completely.
If you genuinely don’t want to side with anyone, I would invite them both and let them decide if they want to come. If one or the other is instant on not going because the other is, and it carries on too long. I would explain that in that case, there will be times that you do things without friend 1 and times you’ll do things without friend 2.