The right side of you topology has worked in the past because you did not need the ability to route between VLANs. I would either introduce a router or switch capable of NAT/PAT and 802.1Q, or connect the DSL modem to your 3750 on the right side of the topology. As your VLAN numbering in the topology conflicts with the text in your question, I'll be referring to the topology.
The latter suggestion is to connect the modem directly to the right (direction) Catalyst 3750 switch, enable Layer-3 functionality on that port and configure trunking on all interfaces connecting the switches. From there, you can define VLANs 2 and 3 in the local VLAN database, configure a VTP domain and distribute the information to the rest of the Catalyst switches.
Consider refining your approach to the solution. Notice that VLANs 2 and 3 are on the left side of the topology. If they have to communicate, be sure to configure the left 3750 switch accordingly, or the traffic will have to cross over to the right (direction) 3750 before being routed back to the left side.