I have a few small suggestions; some that I personally think might be useful.
When selecting pets to put in a party, it would be neat if it had a icon or something to indicate that it is already in a party and maybe something to indicate what party it is in.

Secondly..when a particular party is "Active" (assuming you have more than one ) I would think it helpful to show the name of that active party instead of it just showing as "Active Party" on the top of said pane...sometimes one forgets especially if you are training a set of pets for a particular skill or something.

Perhaps it might also be helpful to have a small button on the top of the "Active Party" pane that lets you actually save any changes to that actual party rather than having to risk accidentally changing your "Main Party" when you hit the "Save Preset" button.

See.."Main Party" shows by default in the preset drop-down box and there have been many times I made a change to my active party (a party other than my main) and then hit "Save Preset" only to discover it made changes to my Main party and not the one that is actually active. (Yes, I know I could have been more careful and selected my active party name).

Anyways..these are just a few things I feel would make things easier.

P.S: I am referring to the aspects on the "Party" page which can be accessed under the "Explore" Tab.

I am a little confused on what you are asking for specifically, but there will be a brand new Party Manager page coming very soon so hopefully it will improve the situation for you.