An MX record to the router will not work. You need to have them set the MX record to the external IP address for the mail server. An even safer implementation would be to use a mail proxy which will scan and forward emails to your mail server.
First you need to get an external IP address for the server and map that external IP address to the server preferably using a firewall. Then tell them to set the MX record for your mail server IP address instead of the router. It can take up to 48 hours for replication.
This gets kind of confusing for someone just starting out, so I recommend you talk to a networking contractor to help you out. They should know how to secure it and of course make it work. Make sure that the contractor knows what he is doing otherwise, you will get an even bigger problem trying to fix or change things in the future.
If your router external interface is connected to your external IP then your phrasing is correct.
Is your Router just a router? Or is it a firewall also? You need to make sure that port 25(SMTP) is allowing pass-through to the Mail Server IP address(i.e. Protcol SMTP port 25 >>> 192.168.0.1(mail server IP)). Since you are using SBS 2003, Domainand Mail server reside on same machine. There’s no way around this without adding another Server(Non-SBS). I have several customers with this scenario and, all work just fine. If you intend on using OWA you’ll need to point port https(443) and possibly http(80) to the mail server also.