Glad you solved the problem and the code worked.
Check these subjects:
-Input protection diodes.
Since I know arduino adc only reads 0 - 5 V and using 100,000 gain [ not sure if i can do this] to multiply the signals, if i do, the highest output from the sensor goes to 50V and that will harm the arduino.
Then you don't need 100000 you need only 10000 to get the 5V you want and not 50.
Check the datasheet of your instrumentation amp to see if the gain can be set to 10000. I'm using right now an AD620 with a gain of 2000 with no problems. On it, the gain can be set to 10000 according to the manufacturer.
For the precision rectifier if you are concern about temp dependency of your whole system transfer function select a low offset temp drift opamp and low temp coefficient resistors. Correcting temp drifts later on will be time consuming and can get pretty ugly.
I still don't understand why you are getting such low voltages with a gain of 1000 already and how could you read them without a precision rectifier??? But I'm not there.
-Are your TX and RX too apart from each other?
-Do the RX coils have enough turns?
-Are you feeding the right power to the TX coils?
-Are the frequencies correct?
With such low voltages and coils as pick ups, if you are anywhere near public broadcasting stations frequencies and/or distances you will have problems isolating your signal from the interference from theirs. Its always better to have a strong clean transducer signal than having to amplify it too much to keep the S/N ratio under control. Maybe you can improve your transducer performance somehow and get a stronger signal so you don't need to amplify that much.
I wish I can think first and do it rather than do it and think later.....
That's common occurrence for many of us, including myself. The reason being lack of patience... That condition improves a bit as you get older though.