Pets never lose aggro on the boss, it's just a large packs of trash problem, and even then, usually if you're just not paying attention.

The third pull in HoV (that nasty one with the dragon) is definitely rough because you'll have to heal the pet(s) quite a bit. Misdirection on pull and a growl or two might be enough /shrug. This will get better with gear as the pet gets hardier and misdirection damage gets higher, so might not even be an issue for you.

I'm still figuring it out, but I think using tenacity pets just for the nasty pulls w/ binding shot might make it a lot easier. Then just swap back.

Druid is pretty easy and mobile. I generally drop the green AoE, hot up the tank pet, and have swiftmend at the ready. Usually that's it for trash. Wild growth yourself if you're taking a lot of AoE (like mariner).