Will These Electrical Panels Support Hot Tub?
I assume the 2nd pic is the sub-panel in your garage?     If so, you should be fine installing the breaker for the hot-tub in the garage, since it has a 125 amp feed.  That is unless you have lots of other simultaneous heavy loads, which I don't see breakers for. Just because the amperage of the breakers adds up 170 amps in that panel isn't a problem.  Panels are over-subscribed all the time.
Using the capacity of every breaker at the same time, is a virtual impossibility.
The heating element size in common hot-tubs is 4 - 5.5 KW which is 16.6 amps and 23 amps respectively. And it will not nearly be on all the time.  Additional draws will come when you use it and start running pumps.  But the total draw will be less than 50 amps.
Again, just because you have the circuit capacity doesn't mean you are using it.  If you were using all the capacity of every circuit in your house (ignoring the fact the main breaker would trip), you'd need a very large loan to pay your electric bill!