H-Bridge Power Supply Erratic Behavior
The current regulating devices in your link are rated at 5A not 0.5A but your real problem is that the IRF2110 won't work at the slow speed/rate you are using it it at I believe. It uses a technique called bootstrapping to enable the N channel MOSFET to be used as the high-side driver and this is your basic problem.

Normally folk use these devices at PWM rates over 1kHz but your rate is only about 4Hz. This means the top MOSFET won't be driven properly and will heat up as per the detail in your question.

It sounds to me like you need a H bridge that comprises N channel MOSFETs for the low side and P channel MOSFETs for the high side.