An open-source finite volume alternative is OpenFOAM (www.openfoam.com), which is focused on fluid dynamics, but also includes a solver for EM problems.
sparselizard (www.sparselizard.org) includes edge shape functions specially designed for EM problems and also allows in a straightforward way multiphysics coupling, e.g. with fluid equations. It is a c++ library but the syntax is made to be easy to use.
On the website there already is a 15 liner EM as well as potential fluid flow example.
After one more year of active development it seems what you (were) trying to do at the time of your question (i.e. EM + fluid fem simulation coupled) is becoming very straighforward with sparselizard now.
There are quite a few readily usable and commented EM examples and several fluid examples online now (www.sparselizard.org).
Concerning your concern about no available fem tool for general and usable multiphysic simulations I am working hard on this since 2 years and it seems this is more and more achieved: the online available set of physics simulation examples gets larger every month while the code efficiency is even further improved (almost entirely multithreaded execution now) while the documentation and code readability is kept at a very high level. No compromise is made on code validation: the examples online are carefully validated.
I would in any case appreciate any feedback on the library.