3 access points, two standards and a bridge

I wonder if anyone could tell me if the following will work:

[router]--wire--[AP1]~~11g~~[AP2]--wire--[AP3]~~11b~~x

I'm looking at getting two 11g access points and I have one 11b access
point, the 11g APs I've looked at can work as bridges or APs. I have a
few 11g/b network adapters and a few (old) 11b ones.

With AP1 I would obviously then have an 11g network. Connecting AP2
wirelessly to AP1, I'd like to use it as a bridge to which by wire I'd
connect my old 11b Access Point (AP3). This I'm hoping will provide me
additionally with an 11b network.

My router and AP sit in a corner in the living room on the ground
floor. Our studies are on the first floor where the signal is good or
excellent but in the garden the signal is usually only fair or bad. So
by bringing my AP2-AP3 combo online I could site my 11b network higher
up and further back in the cottage, which will give me better network
coverage in the garden.

Before I go and by two more APs I'd like to know if anyone has done
this and if:
1.) it works as I'm hoping
2.) running 11g and 11b together will cause problems for the signals.

Thanks,

T