Re: So what are the alternatives that people recommend?
When Dyn pulled this on me last year I paid them for a year, while I found an alternative, but have now switched to no-ip. I am now ignoring Dyn's nagging to renew, they'll get the message eventually. One advantage of no-ip is that many of the standard home ADSL routers support it, so there's no need to add some custom server & scripts. Just configure the router as you used to for Dyn.
Sure, there are technically more sophisticated approaches, but for home use to let me connect back to my Mum's network when I need to, KISS is still the best approach.