The ever–increasing demand for mobile content delivery and multimedia services is bringing renewed interest in multicast communications in Wi–Fi based WLANs. Nevertheless, multicast over Wi–Fi raises several challenges including low data rates and coexistence issues with other unicast streams. Some amendments to the Wi–Fi standard, such as 802.11aa, have introduced new delivery schemes for multicast traffic as well as finer control on the low–level aspects of the 802.11 medium access scheme. However, the logic for using such features is left to the implementer of the standard. In this paper we present SDN@Play Mobile, a novel SDN–based solution for joint mobility management and multicast rate–adaptation in Wi–Fi networks. The solution builds upon a new abstraction, named Transmission Policy, which allows the SDN controller to reconfigure a multicast transmission policy when its optimal operating conditions are not met. An experimental evaluation carried out over a real–world testbed shows that our approach can deliver significant improvements in terms of both throughput and channel utilization compared to the legacy 802.11 multicast scheme. Finally, we release the entire software implementation under a permissive APACHE 2.0 license for academic use.