Hi - sorry to hear about the condition of your daughter, seems she is getting a lot of love and attention - kudos to you!
How would the system notify you was the question. You did not mention any output channel for the device.
This testing does not need to be running all the time, may be checking once a minute is enough - which should help with battery.
You don’t need 16MHz either - a 8Mhz / 3.3V Unit would also save battery
So 8MHz pro mini with removal of the led and regulator and powered with a NI-MH 3.6V or LI-ION 3.7V. If you can turn off the sensors, during sleep you’ll get a current draw of 1.5µA - that’s very low.
Measuring humidity can be done with wires and a variation of conductivity.
if you look for "smart diaper" you'll see ready made solutions.