HTTP redirection isn't too bad.
But I'd say no for a dynamic IP.

Generally, this is how things work:
User enters domain name » User's computer finds the IP through DNS lookups » User connections to IP (server).

Note that the DNS lookup is often cached, and at multiple levels (local computer cache, proxy cache, ISP cache etc).  So often, when the user types the domain name, the computer just directly tries to connect to the IP.

Your thing works like this:
User enters domain name » User's computer finds the IP through DNS lookups » User connections to IP (this is an intemediary server) » Intemediary server returns a response which asks the client to make a request to a certain IP » User connections to the IP.

^ It works because, although the DNS resolution is cached, the response the intemediary server gives isn't.

Your best option would be to try to get a static IP if possible.