Right. The redirect to the fight was a temporary but necessary measure while we were developing the horses traveling to avoid failures when the party is stopped in fights. This has been already developed (it has been a big part of the ambushes update.) Soon in very few days you will see important changes in the party screen: several horses, points of battles where the horses will meet... and of course, this eventual redirect to fight screen has been already removed in this update, as it is no more necessary.
This redirect was the reason of the first part of your report: when the party you are viewing enter in combat, as you cannot be redirected to their combat, you were taken to your party screen. In fact we expected a bigger use of the party's walls when two fighting parties will be fighting one to other (besides that someday we will add also mini-chat for the party members in the battle).