Do you know which provider is running the nameserver for your domain? This should be configured somewhere at Network Solutions as something like ns1.somehost.com, ns2.somehost.com, etc.
I ask because the tidyest solution for you is to change the nameservers for your domain to DreamHost's and let the DreamHost system automatically manage the DNS records for your web hostnames. You can then do a manual override of the mail records to your old host.
The alternative is your original proposal to manually override the DNS records for web hosting to the DreamHost IPs. In order to do that you'll need to have added the "real" domain to your DreamHost hosting via "Domains>Manage Domains>>Add New Domain / Sub-Domain". After you do this, back in "Domains>Manage Domains" you'll see the domain listed in a table. If you click on the "DNS" link, you'll see the DNS entries for that domain, including the IP address of the web server handling your domain. This is the IP address that you'd need to enter into the DNS records at the official nameserver.
BTW, it's worth noting to you that the domains and subdomains that you host can end up assigned different IP addresses from each other. They'll frequently get the same one, but for mysterious reasons they'll sometimes end up with different ones.
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