Does converting 12V DC to 110V AC really increase the available watts?
Your maths is wrong.

100 Watts generated by solar power at 12V.

Your 8.33 amps is the correct calculation.

The mistake you have made is assuming that this current stays the same value when added to the 110V source. You cannot just connect the systems. To feed the 12V (DC) into the 110V (AC) you need to convert them to the same thing - usually the 110V AC. This means using some form of converter (basically a transformer with the DC turned into AC by transistor switches). The POWER OUT will always be less than the POWER in so that at 110V the current will be less than 0.909 Amps NOT 8.33 Amps.  (Vin * Iin >= Vout * Iout)