How to wire 2 switches with 1 hot wire?
You definitely have a hard one here.

And it really isn't helping that "the last guy" was plainly nuts, because it casts shade on all the previous work.  

The best we can hope is "the last guy" changed the switches for aesthetic reasons, and either bought the wrong switches or connected them wrong.   

But we have a few clues.

First, all the white wires go together.  There are lots of other arrangements that are more complicated, but fortunately, we don't have any of those.  No switch loops, no weird 3-way stuff etc. (well possibly one straightforward 3-way).

Second, the hoppy white wire which goes to both switches -- that is certainly an always-hot supply wire.   Let's mark this one black with tape because we know it's always-hot. 

Third, you detected a different always-hot supply wire.  Let's also mark this one black with tape.  That tells me the above (hoppy) wire is actually carrying always-hot power onward to other locations.  This is a huge lucky break.  Normally onward wires are difficult to identify. But now we know (well, we hope) that no matter what, the above two wires are always-hot, must go together, and they must land on one terminal on each switch.  

Now, we have 3 wires remaining, which is one more than we expect.  Weirder, there are two /3 cables in the box.  What I suspect is that the three wires go to: 


One of the lights or switched receptacles
Another light or switched receptacle
Onward always-hot power to other outlets. 


Well, honestly, it doesn't matter if we switch all three of them.  

So I'm inclined to have you get a duplex switch (2 switches on 1 yoke) and do exactly that.  And see what happens.  

Hooking it up

So... the two "supply hot" wires need to connect to each other, and to 1 terminal of a 1-way switch, and to the common terminal of the duplex switch.  You seem to know how to do that well enough.  I would actually have the "loop through" wire go to the duplex then onward to the single switch, that'll let you finish with an extra terminal for always-hot.  

Each of the 3 remaining wires goes onto one of the switch outputs.  

Now, you will have 3 things under control of switches.  Two will make sense, and on one, it will be obvious that it should be always-hot.  Once you identify it, move that wire to an always-hot terminal.  At that point you'll have 2 things switched, and you can go back to plain switches.