If you cannot connect the AirPort Express to the AirPort Extreme using a wired Ethernet connection, then a pair of Ethernet powerline adapters might be able to send the Ethernet signal over the AC powerless in your home.
The computer / electronics superstore near you will have a selection of devices from which to choose. Ask the guys there what works well in your area.
The theory with these devices is that you already have the wiring in place, you just need the adapters. In practice, things do not always work as well as the theory might suggest, so if you decide to try a pair, it would be a good idea to understand the store's return policy in advance.
As you already know, trying to extend by using a wireless connection will degrade the performance of your network. As more devices try to connect, the problems accelerate. I've been there, tried this a number of times. it does not work very well in my opinion. If there is a secret, I have not found it, but maybe another user has and they will post here.
in the meantime, If you want to continue to try to extend using wireless, all that I can suggest is that you experiment with different locations for the AirPort Express. Keep in mind that the Express can only extend the speed of signal that it receives, and the signal has already slowed down quite a bit by the time that it reaches the Express. The whole setup acts like a big antenna, so interference from other networks and cordless phones is picked up easily extending using wireless....another item that affects performance that we have barely touched upon here.
Ultimately, you will have to make a choice between performance and convenience. It's your call. Good luck.