Here is something you could try. Get the Android tablet working with the original router and make sure you can surf the internet. When you are sure it is working fine check the network settings for that network:
1 Click on your Settings Icon (usually a gear symbol)
2 WIFI will be "ON" and the name of the network to which you are connected should show "Connected". Other networks your tablet has seen will be shown but have "Not in range" or "Saved, secured with WPA2", or similar.
3. Long-press on the name of the network to which you are connected. A window should pop up with two choices; Forget Network and Modify Network.
4. Press on "Modify Network" to display a new window showing the IP data. You may have to click a box halfway down "Show advanced options". It should show your IP address, etc.
5. Note your settings.
Proxy should be "None"
IP settings is likely "DHCP"
IP address will be something like 192.168.x.x depending on how your router is setup. For example mine is 192.168.1.41 (but yours could be 192.168.0.5, 192.168.1.5, etc. The important thing is the 192.168.x.(something).
The gateway for mine is 192.168.1.1 but if my IP was 192.168.0.41 the gateway would LIKELY be 192.168.0.1
DNS 1 in my example will be 192.168.1.1 (same as the Gateway)
The main thing to note is your IP address, Gateway (which is likely 192.168.<same as 3rd number of your IP address>.<something(but likely 1)>
DNS 1 should likely be the same as Gateway.
6. Cancel out of the screens (don't save).
7. Turn off the Android WIFI and get out of settings.
8. Go close to your WIFI extender and turn the WIFI on again.
9. Go into Android settings and check the WI-FI list on the right. See if the tablet is now connected to <yourNetworkName_re2(i.e. the extender)
10. if it is, long press on that network name. A window should pop up with two choices; Forget Network and Modify Network.
11. Press on "Modify Network" to display a new window showing the IP data. You may have to click a box halfway down "Show advanced options". It should show your IP address, etc.
12. Check the settings. Your Gateway and DNS 1 should be the same as your router network above, but I think the IP address should be different(but I'm not sure).
The other thing to try is:
1 Click on your Settings Icon (usually a gear symbol)
2 WIFI will be "ON" and the name of the network to which you are connected should show "Connected". Other networks your tablet has seen will be shown but have "Not in range" or "Saved, secured with WPA2", or similar.
3. Long-press on the ORIGINAL of the network (i.e the router). A window should pop up with two choices; Forget Network and Modify Network.
Click "Forget Network"
4. Long-press the extender network and forget it as in the above step.
5. Go close to the extender network and connect to it.
ONE OTHER THOUGHT:
For the network password you state the extender network has a different password. Check on your instructions, perhaps it should be the same as the router network? (i.e. not talking about the Admin passwords to manage the devices).
I hope this is not too confusing.