The decision about induction in my mind boils down to one question / item.
Are you planning to always be hooked up to electrical power when you cook, or able to run a generator?
If not, I'd recommend going with gas.
Induction makes the pan hot, not the cooktop surface, so control is better than traditional electric stoves, but still less than gas.
Convection/ Microwave ovens are superior to RV style gas ovens. Period. However, they also require substantial electrical power.
Alternative cooking such as a Coleman stove may work, but she is going to want to use different pans for the outdoor cooking.