Ed Beal nailed it: it needs to be a subpanel. That will serve you so ridiculously well that you'll be back here saying "enough already!"
First, tear out that 30A Breaker! Common plug-in circuits are only wired for 15A or sometimes 20A (if they have the larger 12 AWG wire) and you're tripping a 30. This is how you burn down houses. Replace that breaker with a 15A And Stop Overloading It. This is the work of the last guy, a fool who upsized the breaker because he was sick of it tripping and just kept upsizing breakers until it stopped tripping. He couldn't be bothered learning how not to trip breakers.
Now let's talk about what options you have for that 50A circuit (assuming it is a 50A circuit -- is the wire really 6 AWG? Or did the same fool put a 50A breaker on 8 AWG? (if so it must be a 40A breaker, but that won't affect anything that follows.)
Option 1: Pump only
This pump may not enjoy American 60Hz. However you hook up the two hot wires (black/red) to hot and neutral on the pump. Doesn't matter which. White is unused, cap it don't cut it. Bare/green ground goes to earth on the pump. In your main panel, change this circuit's 50A supply breaker to a 20A 2-pole GFCI breaker. Yes I know how much those cost.
Option 2: Dog dryer(s) or A/C; pick 2. No pump.
This scenario lets you run 2 dog dryers, or 1 dog dryer and 1 AC. You cannot power the pump.
In the main panel, change this circuit's 50A supply breaker to 20A 2-pole. It doesn't need to be a GFCI breaker, but if it is, you won't need GFCI receptacles.
Back in the room, bring the fat #6 cable into a junction box. From there, use #12 cable to fork off 2 more junction boxes. Each of the end junction boxes gets a 20A NEMA 5-20 receptacle, and it must be GFCI (except as above). In the central junction box: all grounds go together. All white neutrals go together. Red goes to one of the hot wires from the receptacles. Black goes to the other hot from the other receptacle.
Option 3: Subpanel
This powers both dog dryers, the A/C and the pump at the same time. And actually has a full circuit's worth of power to spare. And it will be a safer installation, as things associated with "wet" will have GFCI protection.
Get yourself a modest sized panel such as a Siemens 12-space main-lug panel. Don't go smaller than 12, you'll hate it later. So this is what it looks like. Neutrals and grounds omitted for simplicity.
Now let's take a look at what's happening here. You notice the odd bus routing in there? That's because the panel has two poles and the buses are arranged so adjacent breakers are on opposite poles. I also took the liberty to use black for wires on pole L1 and red for pole L2.
Everything but the A/C needs GFCI protection. For the pump there's no choice but a pricey 2-pole 20A GFCI breaker. (15A would also be acceptable, it's just such an odd duck that I hate to spend $80 on one.)
For the dog dryers, I used 20A plain breakers the cheaper GFCI receptacles, note they are the 20A variety. A 17A device needs to use the funny plugs with sideways neutrals. Since the dryer maxes out the circuit, I would have preferred to use 1-socket receptacles (like for the A/C) - but those are not available in GFCI @ 20A. Don't plug any other big load into these dryer circuits! Cell phone chargers and LED lamps are fine.
The A/C unit gets a 15A breaker and a 15A single socket. You could also use a 20A breaker and 20A single socket (with the T neutral). The single socket is so we can avoid GFCI.
Now let's tally up the amps on each pole. For continuous loads, we must derate by 125% - so your 10.8A air conditioner becomes 13.5A derated.
- L1: 4A pump + 17A dog dryer + 13.5A air conditioner. Max load on L1: 34.5A.
- L2: 4A pump + 17A dog dryer. Max load on L2: 21A.
It would be bad if both dog dryers wound up on the same pole with the air conditioner, so that's why I put their breakers adjacent. In fact, just tape them together. No need for a handle-tie.
Let's assume further that the last guy was a fool and used 8 AWG cable on his 50A circuit. 8 AWG cable is actually rated for 40A, and in that case the breaker in the main panel should be changed to 40A. Even then, we are in good shape.
We could definitely support one more 20A circuit on the L2 pole. And here's an idea: the circuit that comes into this room that is constantly overloaded: cut it in two at some middle point. Feed half from the main panel and half from this panel. It would really matter where you cut it, so you would have to do a careful load survey of the sequence of the outlets and where the heavy loads are.
If the service is honest-to-goodness 6AWG 50A, then you could even support 2 more general circuits in addition - though not at max load of course. It's OK to oversubscribe panels a fair bit; you just can't do that with known loads.