I agree with the above.
OP, We don't know these people so we are making judgements based on a few things you have told us.
I think for friend1 to move their child to a different school in year 6 is a severe over reaction, over an issue of non inclusion in group playground activities. Having taken such a severe step, to then say to friend2 that she hopes the childrens' relationship, outside of school, will be enhanced, is just disingenuous! Who on earth would think that. Its just like rubbing salt in a wound. How you can expect friend2, to ignore the accusation that her child is such an extreme bully that friend1 has had to change her sons school and still continue to be friends is just nonsensical, whether it is true or not.
I also think it is strange that friend1 would want to be in a friend ship group with friend2 when her child was so badly being bullied by friend2's son, that she was having to change his school.
I think that some friendships are just not meant to last.
Whilst friend1 has said, all she is is expecting from friend2 is a cordial and polite relationship, this is not a true friendship. I know there are 5 of you, but not all of you are going to be available to meet up, so there could be just 3 of you say, which would be very uncomfortable for friend1 and friend2 socially.
Friend2, is not saying you can't see friend 1.
Out of curiosity, did friend1 talk about the bullying prior to moving her child to a different school?
Who told you about the bullying? Friend1 or friend2. Has friend1 not told you how bad it was, in order to be diplomatic?
I would say, there's no coming back from this. See friend2 and friend1 but not together. The group is too small and it is too awkward for the friendship group to continue as a fivesome.