Electronic – Bipolar switched-mode power supply

To a first approximation you should be fine. As long as the inductors have decent frequency response, so you don't get much in the way of current spikes, the capacitor will be OK, and does not need to be a low-ESR type. But a better cap, one specified for use in switching applications, would be good insurance.

But hey, the worst that can happen is the cap blows up. Just put a paper cup over it. These things don't send shrapnel flying when they fail.

You can do them both in parallel on one circuit. You just need a large (40A) MOSFET or IGBT. IN this case, MOSFET would be far better, as you can just use an opto-isolator working from the Arduino 5V PWM to the supply voltage of the MOSFETs. You could also use multiple MOSFETs in parallel to achieve the same thing, though you may need a greater turn on current. You could also try cooling the MOSFETs fom the Peltier modules, which would use more power, but keep your MOSFETs nice and chilly. If you do not cool them with the Peltiers, make sure the MOSFETs have a large heatsink.