Usually you'll want to have Warrior = Dark Knight > Gunbreaker > Paladin pull the boss, in the hierarchy.
Typically though in normal mode stuff, you'll find said hierarchy isn't really followed, but usually dictated by which tank is better geared (more HP) and sometimes you'll have some tanks charge straight in as soon as the barrier goes down. You kinda get used to it the more you do it.
Do keep an eye on stances as you load in as well, as the other tank may have theirs active which can be an indication that they want to tank.
Aggro management is a non issue if you do your correct rotation. This is something that is highly encouraged that you are doing it correctly, and not "freestyling" or doing what you might think is right. Damage = Enmity, so doing poor damage by not doing your rotation properly means you generate less enmity than other tanks, and therefore can rip aggro from you quite easily.
Usually the OT should use their stance once MT gets a decent aggro lead, to ensure they're second threat in case anything goes wrong, and may save a DPS/ Healer eating a tank buster.
This might also be a contributing factor to your spinning boss issue, where, the other tank is executing their rotation better and or better geared, alternatively some tanks like to spam Provoke as soon as it comes of cooldown even as OT, frustrating but easier to Shirk them if possible, so you don't cause wipes or cause missed positionals for Melee.
Tank swap are usually quite obvious in current content, where, a physical, magical, slashing, piercing or blunt resistance down (red) debuff is applied to the MT. This again takes time and practice to get used to, gotta do it to learn.
OT mitigation you want to aim to have for tank busters to help out the MT, unless you also are targeted with a tank buster (except Paladin, with 100 gauge can Intervention the MT and Sheltron). If you're not needing
OT mitigation outside of that, use to help mitigation as long as it won't leave you short, e.g don't spam TBN on the MT or you'll be wasting mana.