Is there, by any chance, a mod that prevents you from so easily being arrested for accidentally hitting guards during the MQ missions?

It happens. You should get a warning before they actually arrest you. Something like "I'm on your side!"
If that happens just yield to them if they attack you. (block plus activate)

I do not know of a mod but that does not mean there is not one out there.

For a second there I thought there was going to be a name conflict with one my mods. I have one called Friendly Fire for Frans on the Nexus. Sorry, but it doesn't address what you want. It just adds some non-hostile NPCs to various spawn points in the game.

forgot about the yield thing. thanks.