Need a little advice/help here. We're trying to use two separate Internet connections, through a single switch, with static IP for the T1 and DHCP (using a router) for the DSL. But we are also trying to keep file sharing, network printing, and VOIP phones all working.

I have included a diagram with how we're trying to set our office up, and I'll be more specific with what we're trying to get working:
A. T1 line, connected to a switch, with each PC in the office connected to the switch for Internet access and file sharing. (blue line)
B. DSL line, connected to a router, connected to the same switch. (green line)
C. VOIP phones, connected to switch, using DSL through the router with DHCP (green line)
D. All PCs able to print to printer that is connected to switch. (pink line)
All the colored lines represent exactly how the network cables are run. The only exception is the PCs - the PCs are connected to the VOIP phones, and then the phones connect to the switch - one cable between each device for everything.
In simple terms we're trying to keep our network functionality (file sharing between PCs, internet access, and printing to a central printer) / we're trying to keep our VOIP phones working / We want only the PCs to use the T1 for internet access / we want only the VOIP phones to use the DSL.
So far we haven't been successful. We're not sure if it's a settings thing, a hardware thing, or other. Is this even possible, or do we need different hardware or a different configuration?
We're not exactly network experts beyond home setup, either. =X