Powering surging trouble

Ok first, thanks for reading my thread. Here is my trouble that I would like someone to help suggest a good solution:

I drive a fair bit for work in my full size cargo van. Which means I have added a fair number of toys to it. I have a nice head unit, good speakers, added two self powered subs, 120v power inverted (150watts), and some really bright driving lamps. Here's where the problem starts, the driving lamps are 100watts each, there are 4 of them. I wired them off a relay which recieves its 12v+ input from the high beams. So when I turn on the high beams the driving lamps illuminate providing me with some incredible high beams. Great! But, when ever my power inverter is on and powering a device, if i turn on the high beams, the surge causes the inverter to fault (i guess from the lack pf power at the battery when the other draw robs its 32+amps for driving lamps). So, how do i go about getting the necessary power to the inverter, without just driving along with regualr highbeams?

Here's my idea. Call it crazy or say it makes sense: Run a power line from batt to inverter, but put a capacitor, like a 1 fared in line, then go to the inverter. Would this not allow proper power to get to the inverter, due to the fact the the inverter will run while lights are on, however for that sudden burst to get the 32amps of light on it seems to just fault the inverter to off.

ANyone else have a better or another idea that could work before i go out and buy a really expensive cap?