The amplifier's plug should "break" the tablet's speaker circuit, directing the output to the external speakers.
When you say you can hear the music in the tablet's speakers, can you also, at the same time. hear it in the amplifiers speakers?
Can you make the problem happen by gently (very very gently) moving the amplifier plug whilst it is in
the headphone jack?
If so It could be either a worn amplifier plug (have you tried a different one?) or an intermittently faulty tablet headphone jack.
If you have tried a different amplifier plug and it is still the same, the problem is with the headphone jack.
Check your warranty and if still valid contact the manufacturer .
As I now understand, you wish to have both your tablet's speakers and your amplifier playing music at the same time.
Unfortunately this is not how a headphone socket is wired to allow. You could open your tablet and solder some wires to the input side of your headphone socket, then pass them out somehow and then connect to your amplifier from those wires. Not very elegant and perhaps may not even work. it is possible the the tablet's audio system may not like having too many outputs connected in parallel at once.
One idea is that you purchase the following
1. A Bluetooth transmitter with 2 connections at once http://www.amazon.com/gp/product/B00NMPK... (this is only an example of what is available, not a product recommendation)
2. A Bluetooth receiver with audio out
http://www.amazon.com/Bluetooth-Receiver... (this is only an example of what is available, not a product recommendation)
3. A suitably sized, powered Bluetooth stereo speaker. (as with above items, your preference)
Then you connect the Bluetooth transmitter to the headphone jack of the tablet, the Bluetooth receiver with audio out to the amplifier input and place the Bluetooth speaker next to the tablet.
Pair the two "receivers" with the transmitter and you should have music at both your amplifier and "technically'' at your tablet at the same time.
There is a "range" limit with Bluetooth to be aware of, among different Bluetooth specifications, there are 2 most popular classes (types) of devices: Class 1: range up to 100 meters (in most cases 20-30 meters) Class 2: range up to 30 meters (in most cases 5-10 meters)
I could not find an App that allows you to use the tablet's Bluetooth and send to two "receivers" at once. Or that you could send music via Bluetooth and connect to the headphone jack at the same time. Apparently the headphone jack overrides Bluetooth in Android!
Hopefully this has given you food for thought and maybe ideas for other options as well.