I'm interested in modeling the electromagnetic fields radiated from an accelerated charge, but do not want to reinvent stuff if possible. I suspect there are software packages already out there which allows a person to provide the incoming accelerating field or trajectory of the charge, and is returned an array of values of the field in some region of space etc.
An answer to this could go in a lot of directions. I think the closest class of software matching the question as asked would be a "particle in cell (PIC) method", see https://en.wikipedia.org/wiki/Particle-in-cell for an overview. It's basically an FDTD-like method, with "particle pushing" (Lorentz forces) bolted on.
However, "modeling electromagnetic fields radiated from an accelerated charge" is pretty abstract, and most electromagnetic modeling software is aimed/tuned at a more specific class of problem.
A PIC method, for instance, would be used to model a high power microwave source (magnetrons etc, a particle beam shaped/controlled by quasistatic magnetic field). But a different engineering problem might be more easily modeled using a different method (antenna radiation is easy to model using finite elements, radar scattering is easy to model using surface integral equations, etc).
Even though all of these scenarios can be abstractly lumped as "radiation due to accelerated charge", each would probably lead you to pursue a different technique.