Yes, 1/8" chains are less tolerant of poor chainlines. They were designed to operate exactly in line, long before anyone thought to have two or more cogs and change gears that way. Hence they will run rough at rather small chainline deviations whereas 3/32" chains were designed to operate well up to around 3/4" off.

An approach that would be cheap but a fair amount of work would be to respace the hub washers and redish the wheel. You may have a washer or two you can move from the axle on the right side of the hub and put them on the left side. You will then have to loosen the left side spokes and tighten the right side spokes to correct the "dish" of the wheel so it sits centered in the frame. This will move the entire hub to the right by whatever spacers you move from right to left. This requires no more than a coupld of wrenches and a spoke wrench but a fair amount of work and work that has to be done right our the results will be bad. If you decide to go this way, stay close here and maybe recruit a knowledgeable friend.

Edit: See if you can find a bike coop or bike repair shop. I;ll bet there is one in your area where you can find knowledgeable folk who regularly do work like this and won't be condescending.

Ben