OK, so you're question refers only to the first website, the one that is physically at your site.
If you're with "network solutions", you probably have a webtool to change your DNS. You could let DNS1 on the T1 and put DNS2 on the DSL. If DNS1 fails to answer, then requests are sent to DNS2. Not very elegant since the DNS might still answer but the physical service could be down.
Instead, I'd put DNS1 on the DSL and DNS2 on the T1. If there's a round robin function, check it. That way, you're telling the servers to alternate when they answer. Remove the "round robin" if the T1 fails
If you have access to DNS SOA entries, set "refresh" , "expiration date" and "TTL" to a minimum for the T1. That way, you're sure that world DNS's will stay rather uptodate.
The "2-day" diffusion time is a general rule-of-thumb. Basically it says that all DNS's around the world will have received their modification during that time. If your visitors are physically located in your area, they'll be uptodated faster since they will probably ask DNS servers closer to you. If you deal with N.Korea, then you'll have to wait 2 days or more ;-)
It will be shorter if you set the SOA entries to a minimum right now.
Actually, you're never sure that the DNS and the website are answering correctly... The only way is to monitor the site directly. There are tools for that (nagios is a well-known GNU tool). What we do here is program nagios to fetch any prefined page on the websites we monitor and check for the existence of a predefined keyword (" doing_fine_thank_! ") that you bury in the HTML code. If Nagios finds the page, hurray, if not, alert.
Since you're interested in large companies

, have a look at microsoft.com NS entries.
you'll note that ns2, ns3 have very different addresses.
If you try a "tracert" command on these IP's, you'll note pretty different routes. Also, if you do a "nslookup" repeatdly on
you'll note that another address is given to you each time. This is a "round robin" destined to alleviate the burden on any given IP address.
;; AUTHORITY SECTION:
microsoft.com. 42179 IN NS ns2.msft.net.
microsoft.com. 42179 IN NS ns3.msft.net.
microsoft.com. 42179 IN NS ns4.msft.net.
microsoft.com. 42179 IN NS ns5.msft.net.
microsoft.com. 42179 IN NS ns1.msft.net.
;; ADDITIONAL SECTION:
ns2.msft.net. 122746 IN A 65.54.240.126
ns3.msft.net. 122746 IN A 213.199.144.151
ns4.msft.net. 122746 IN A 207.46.66.75
ns5.msft.net. 122746 IN A 207.46.138.20
ns1.msft.net. 96160 IN A 207.68.160.190
Cheers