Slitherine

The game freezes temporarily when it shows my opponent's moves in multiplayer. Is there anyway to replay them? I want to just close the game and restart the program but doing that often would be annoying and I'm worried I'd be suspected of cheating.

No, there isn't anyway to replay them.
What you mean with it freezes temporarily? Is it for a couple of seconds?

The visuals freeze although I can hear my opponent's moves. My cursor turns into the blue loading circle (I have Windows 10). It only happens when the game tries to show the opponent's moves. My opponent had the same issue.

I was using mods and he was not.

I disabled mods tonight and I was fortunately able to see my opponent's moves.

I think these were the mods I was using:
- RSM Redux 1.25
- PG Style Strength Plates
- Historical Flag and Insignia Mod 1.30
- the bit unit files from the Battlefield Europe v1.8 mod

I wonder if the mods were the cause of it, and if so which one it may have been?

I tested once more and although it shows my opponent's moves without mods it will crash again if I click... I guess it's an improvement :/

Most probably it's caused by the mods.
On the RSM Redux first post, there's a warning regard memory usage and possible crash/freezing.
I suggest to try the suggestion offered there or then just play without the mods.

I have the same issue with seeing my opponents move without any mods.

Found a solution. Set my graphic resolution away from 1980 to 1080 to the next lower setting and voila no animation hick ups.