Seeking CMS recommendations

This is an open-ended request for recommendations for a dedicated web interface. I'm describing what we're trying to do and what tools we have, and am interested in any input & advice.

We're a public library, and we have a promotional Web site in place that features a calendar of public events. This is built on DotNetNuke, the CMS preferred by the host/developer that we contracted. FMS13 (will upgrade next week to 14) publishes an XML feed which DNN polls every few minutes.

The functionality I want to add is allowing patrons to log in to a site, set up free accounts, log in and register for events. Also some management (i.e. canceling participation, etc.). I think I don't want to try to incorporate that into the existing site - we have many staff members producing information in the existing site, and I suspect that trying to change it in such a fundamental way would upset the apple cart.

So I'm thinking instead that patrons at thelibrary.org who want to register for events will hop over to thelibraryregistration.org, an almost single-use site powered by a CMS interacting with FMS. I don't think WebDirect is the answer, because no user should be able to see the stats of any other user, and because there's enough 'secret' information that should be available to people planning programs but invisible to participants (like if we want to hold back some seats to an event).

So my open-ended question - for a two-way interface like I'm describing, what's your recommendation? I'm expecting to pay for hosting and have to learn an open source CMS. I have some experience administering MySQL and limited PHP.