Unfortunately, with hockey, this can quickly become unmanageable, believe me, I have tried almost every permutation and have yet to get it right. I am not going to say it is impossible, just that it gets very convoluted very fast and there is not enough time for one person to manage it. You might be able to handle a couple of overlapping penalties, but dealing with scenarios of double minors and majors or 3 men in the box it is one big headache.
Basically, with vMix timers and hot keys, you need a separate clock for each penalty, so triggering start and stop has to have it's own key for each scenario otherwise everything gets out of whack.
The simplest solution is to have a dedicated camera on the official clock, make multiple "virtual inputs" from it, and crop each one for the 5 clocks you'll need and use the Multi-view feature to place them where you need them...
If you want to give it a shot and need more assistance, let me know, I'd be happy to guide you through the hot key set up that I've done.


Ice

Well, you're dealing with a 5 on 3 for the balance of the first penalty, so depending on what or how you want to inform your viewers of that will determine how many "clocks" you'll need.
Basically, there are 4 penalty clocks, but with today's crackdown on head shots, you have to account for the 4 minute double minor, which with vMix timers, you cannot easily alternate between 2 and 4 minutes on the same clock (not enough time to change the settings on the fly) so you essentially need to have 8 clocks at the ready,(5 minute majors and misconducts are less common and I have not had a need for them, but they could come into play as well) so you can see how it can be a major distraction to manage which clock at which time when there are more important tasks at hand, namely broadcasting the game. And hence why I say I have yet to get it right during a live broadcast, I've come close a couple of times, but invariably, it gets messed up somewhere. Being able to use the official game clock would totally eliminate those headaches.
Typically, I try to handle the single penalties, but overlapping and multiples I don't bother with too much because of the aforementioned complexities.
And really, in the grand scheme of things, viewers do not pay a lot of attention to the clocks, they will glance at it periodically so it's a nice feature to have, but believe me, you will notice it and stress over it a lot more than they will. My best advise is to keep it simple if you can.
Do you have any recordings of games?
I would suggest trying things out by playing back a game file as if it's live and overlay your clock(s) and scoreboard and you will get a feel for what I am talking about.
If you need assistance, let me know.


Ice

I am not a statistician, but technically, any time a team has a penalty and is at a disadvantage it amounts to a powerplay for the other team. Overlapping penalties can extend the duration of a powerplay with the overlapping time being a 5 on 3 advantage, but I believe the stat would still be considered as two powerplay attemps (or two penalties that put them at an advantage). Some powerplays are cut short because of a counter penalty to the advantaged team. It's still considered a powerplay attempt whether it's 10 seconds or 1 minute and fifty seconds. So it can be a misleading stat when used in that context.


Ice