You need to look at your wireless router.
Does it have different settings?
Does it have an external antenna? If so try moving it around. If not just move the router around.
Can you move the router?
i.e. Use that cable or another to move the router into the Living Room, or
do you usually use your equipment in the Dining Room.
Download some of the utilities like WiFi Analytics and others that give you a wifi power meter onto your tablet or other device and explore where the signal is strongest, and explore what moving the router around back in the Dining Room does. Check with the same devices to see if you are on a channel with interference from other devices, routers, etc.
See if your router automatically switches channels to find the best, the least obstructed or interfered with channel.
If you have access to your router antenna, you might want to put an extension on it, or a bigger antenna. Sometimes just a wire "near" the antenna will boost the signal. Be careful here, you don't want to mess up your router. Check the manual and online to see what to do.
After all that you might need to get another router. A more powerful one. Again, you need to read up on this for the devices you are looking at.
You can put another Ethernet cable into the router like you have already done, and move it into the Living Room and put another wireless router on it since your tablets are wireless.