DW Tempest Regeneration?

Two separate problems going on here.

The Tempest flask abilities have very long cooldowns. If you want them to be up more frequently, you have to find ways to reduce cooldowns, like an Amulet of Cooldown. Unless your problem is stamina? Do you notice your Stamina being low or zero a lot? Perhaps you have the Sigil of the Great Bear equipped. That reduces your stamina regeneration by 1/2. If you don't like that, remove it the next time you are at a blacksmith.

Mark of the Rift is a focus ability. As you do damage to enemies, you build up your focus bar. There are only three things that can make a focus bar go to zero (inactive): you use it, you die, or you have the Rest Easy trial enabled and you visit a camp.

I would suggest checking your settings to make sure you don't have Trials enabled that you don't mean to have enabled, like Rest Easy. If you do want that enabled, then you either have to avoid visiting camps or just accept the fact that you will lose all your accumulated focus each time you visit a camp.

That trial is kind of tricky, because you also lose all your focus by setting up a camp, not just by visiting/fast traveling to one.

I like that plan. Not all the trial rewards seem great but I have gotten a few cool items so will try your tip!