It sounds like you have the network part of the problem worked out.
but my local network can only access the internet and not the public network
To help with this, we'd need more information about exactly what works or doesn't work.
If the problem is that clients using web browsers can't browse to hosts on the 172.xx.yy.zz network, you may need to customize the SME server proxy settings:
http://wiki.contribs.org/Firewall#Bypass_Proxy (this seems unlikely since you say the SME server can access these hosts OK).
If the problem is that clients can access 172.xx.yy.zz hosts by IP address, but not by name, then there is a problem with your DNS configuration. Since 172.xx.yy.zz is a "private" network, SME is unlikely to find the correct DNS entries unless you have configured a "Corporate DNS server" or have manually configured all of the required DNS entries on your SME server itself.
There is also the liklihood that the problems are iptables/masq related - by default, SME is only going to allow traffic in through your firewall that is addressed to the primary WAN IP address - all other traffic is dropped.
You may be able to easily customize your iptables by redefining "OUTERNET" in /etc/e-smith/templates/etc/rc.d/init.d/masq/00Definitions (note: I wouldn't try to do this by resetting "ExternalIP" in the configuration database, as I think that value is used to configure the WAN NIC). Or, you could need to rewrite major portions of the masq templates, or create custom template fragments for the second WAN IP.
The "official" (ie, most common) answer to all dual-wan questions over the years has been "SME doesn't do dual WAN or load balancing, use an external hardware solution".
You should be able to find lots of discussion about this by searching the forums for
"dual wan" and
"load balanc*".
The "coovachilli" contrib implements a 3rd NIC in a SME server, and may contain useful code:
http://wiki.contribs.org/CoovaChilliThe easiest solution would be (in my opinion) to get another 172.xx.yy.zz IP address and use an external PPoE router for Internet connectivity, or get a dual-wan router and move both internet connections off of the SME server (either putting the SME in server only mode, or leaving the SME in server/gateway mode and using a 10.a.b.c segment to connect the SME WAN port to the dual-wan router).