Having problems extending wireless network

Question

I'm trying to extend a wireless network using a number of bits of hardware and would like to know what is the best way of doing it. I've had a good play around with things already, and have read a few tutorials/forum posts but I don’t think I've quite got it right.
The problem:
The current position of the wireless modem/router is in an upstairs room at the front of the house. While this works well with internet connectivity generally (Apple TVs are connected wirelessly in two upstairs front rooms and the living room downstairs, also at front), there is poor signal at the back of the house downstairs where we have another Apple TV that keeps dropping out.
This Apple TV is on the other side of what was the house's external brick wall (the house was extended, so this is now a kitchen/diner that is in a conservatory extension). So a floor, some distance and a brick wall separate this Apple TV.
What I have tried:
Initially I tried using an Airport Extreme Base Station (AEBS) to extend the BT Home Hub (BTHH) signal but had problems with this. According to BT, it should not be possible to extend the network in this way. So instead I tried this:
In upstairs front room:
* BTHH - transmitting 1 wireless signal (which I *could* use but …)
* Connection from BTHH ethernet into AEBS which is then transmitted wirelessly (And *this* is the wireless network I will use for Home Sharing/Apple TVs)
Downstairs, near back of house:
* An old Airport Express (first gen A1088 device), which I configured to extend the existing wireless network (the one transmitted by AEBS, not BTHH). No physical connections here - it's just done wirelessly
This *appears* to be OK, at least from from Airport Utility tells me (I used an older version - 5.6 - to configure the Airport Express, V6 to configure the AEBS). However, the proof is in the pudding, as they say - the Apple TV with the weak signal remains weak (3/5 bars according to Apple TV signal strength indicator), despite the Express being just a couple of feet away inside the house.
So, what can/should I do?
I think I have some more options. I have Powerline sockets that I can use, so I could connect ethernet in the upstairs room and then have the socket downstairs plug straight into the Airport Express.
What is the best way to set it up?
BTHH ---- ethernet ----> [Powerline] ---- ethernet ----> Airport Express
BTHH ---- ethernet ----> AEBS ---- ethernet ----> [Powerline] ---- ethernet ----> Airport Express
Or is there a simpler way I could do it?
I know that I *could* do this:
BTHH ---- ethernet ----> AEBS ---- ethernet ----> [Powerline] ---- ethernet ----> Apple TV
And have that TV use a wired connection instead of wireless, but I'd prefer not to do that for a couple of reasons:
1) The TV is against a wall, with limited space behind for cabling/sockets and there is no immediate power supply (so I'd have to run it all through trunking)
2) It's better if I can extend the wireless signal generally, not just for that Apple TV, but for all devices that might need to connect at the back of the house.
Appreciate any suggestions of what I can do here. I know this is a long note, but I wanted to be clear about what I have tried, what I've got at my disposal, etc.

Answer 1

Thanks for the welcome.
I have checked the settings and have set both up from scratch a number of times. The TC is set to allow the network to be extended and the Express is set to extend the network and to allow wireless clients.
I have also tried a number of different positions for the Express including in the same room without improvement. The network extension does work but with a significant deterioration in network performance when connecting via the Express. I would expect some deterioration in performance for the signal to pass from Express to TC but this seems extreme. The effect is even more pronounced with iPhones (3GS, 3G and 2G). the connection is actually quicker over the mobile network even for the 2G phone.
Cheers