Guild Wars 2

It can be a mix of the suggested ideas.
For example : F3 skill gives pet a buff to avoid damage and so does dodging.
It doesn’t have to be the same buff, and there can be a shared cool-down to both mechanics or pet’s endurance consumption.

Edit : Pet already gets 2second protection on dodge if traited.

But there are 2 leaps… Which means even though the damage is higher the DPS is not

The auto attack on both weapons have about the same numbers, only difference being the attack speed. And the GS’ skill 2 makes up for that difference.
Only other difference i see is how you want the evades/leap to work (considering skill 1-3 of both weapons).

They have pretty much the same DPS if you consider GS’ skill 2.
I’m pretty sure the sword’s skill 2 and 3 have less dps than the skill 1. (not tested)
While GS with skill 1 and 2 has about the same DPS as sword’s 1.

Now, we need to know which of them stack together and which don’t.

I don’t like the idea of getting a buff other than invulnerability+prevent the pet from attacking while the buff is active with a cool-down to it;

Because I think it can get overpowered if the buff stays, since we’ll just call it back to buff the pet with swiftness or aegis for example then send it back.

Unless it’s dungeon exclusive there might be a balance issue.

Vox Hollow.2736:

[…] making the Return mode involve a tighter, firmer, closer handle on where the pet is located in relation to you – so that when you move to avoid an AOE your pet is close enough to your heels to avoid it too. […]

Something along those lines would be great too. So pet can live through an AoE targeted at the player when it’s on ‘Avoid Combat’ mode.

The primary use to this would be to keep buffing pets alive.

It can be done through adding some temporary buff to make it avoid damage when the player dodges (when it’s on passive) or as it was said making the pet stick close enough to the player so it avoids the damage if the player succeeds to exit the red circles.

Edit: This way there will be less micro-management to do when pet is not in combat.

Maybe adding something similar to a downed-state;
When pet gets killed it can have a chance to deal extra damage or recover;
It might be something like the F2 skill being replaced by something more defensive;
It can be exlusive to dungeons too so it doesn’t break the game balance.

You can map stow weapons to a key which cancels the current action (the same way Esc does)

1second dodge on callback (F3) every 5seconds on a trait?
Just some random numbers. You get the idea.