Do you have a specific trial you're having trouble with, or just in general? The final trial in the Stormblood storyline is a step up in difficulty, so if its that one, you are not alone.

One thing you don't need to worry about as a WHM is stacking issues. Unlike shields, Medica II and Regen stack with each other. If both of you use it, people get both effects. You can wind up with overhealing that way, but in a DF trial, that's a fact of life. It's not the end of the world and not something to stress over.

You don't want to constantly use Medica II because it can get expensive MP wise, but if it's the tool for the job, use it without worrying about the other healer. If they also use it, you don't need to follow up with another AoE heal, and if they're having issues with mechanics/death, you can follow up with a Medica and then Plenary Indulgence (which is free and will heal for a fair bit after two other AoE heals). Those three combined will get the group from near death to near full in anything outside Extreme/Savage mode, and you can do it yourself. You simply stop the second cast if the other healer also gets one off.

For the tank, keep Regen up as much as possible, as that helps every healing situation (including another WHM, who can put their own Regen up). You can try talking to them and coordinating, but in a lot of DF trials that can fall apart when stuff goes wrong, so in those I tend to favor simply doing the first cast and canceling the second if they help out. It's easier to react to that than it is to coordinate it without voice chat, IMO. It's also something that comes with experience.

I will say that if Medica II still has lots of time left on the HoT part, you don't want to cast it again. Medica (and Cure 3 for a stacking mechanic) put out more immediate healing, and overwriting the HoT with another one is just a waste of MP if there's enough duration left to bring people back up anyway. If it's down to 5 seconds or whatever, then you can overwrite it.

But if you can't trust your group... well, then you have to heal them up. In that situation, use Lucid Dreaming before you're at half MP, since that will let you get it back faster. Use Thin Air to Raise people, or for big AoE healing segments if you have a Red Mage (since they can raise people very quickly). Don't forget about PI for the extra top up.