Is most of the software used for simulation and trajectory planning built in-house, or are there some industry standards?
That's not an either/or question. The answer is "Yes".
First off, there is no single tool that can answer all questions with regard to spaceflight. Drastically different tools were needed to plan the trajectory of Cassini–Huygens to Saturn, to model the detailed behavior of Huygens on its descent to Titan's surface, to perform hardware-in-the-loop simulations of the vehicle, and to develop best estimates of trajectory for the vehicle.
Organizations that do this professionally have been doing so for a long time. The tools used were in-house, custom-developed tools. Some commercial tools do exist such as STK and Matlab/Simulink, but these are fairly new compared to the 50+ year history of spaceflight. Some organizations are turning from their custom tools to commercial tools, but typically only on well-contained problems where the commercial tool does the job right out of the box. For a complex simulation project, the costs of maintaining those custom tools and modifying them to exactly suit the needs of a new simulation project are small compared to the costs of number of licenses for those rather expensive commercial tools.
Just to give an idea of the number of those in-house tools, The Jet Propulsion Laboratory uses SPICE and GIPSY-OASIS for some of their work in this area. JPL uses yet another set of software to generate its Development Ephmerides. The NASA Johnson Space Center uses Copernicus, Trick, and JEOD for some of their work in this area. Every NASA center appears to have their own sets of homebrew tools. The Department of Defense has multiple sets of tools. So do the European Space Agency and Roscosmos.
One reason for the number of tools is that the people who use those tools have deep knowledge of how to use them. Switching to something else would be extremely costly. Another is a bit of a "not invented here" attitude.
Yet another reason is secrecy. If you look at STK, you'll see that large chunks of it are off limits to non-US organizations. The same goes for many of those tools developed at NASA. The reason is that the technology that enables accurately planning a vehicle mission to the Moon (or beyond) also enables enemies to accurately plan a missile mission to some US city. Exporting those technologies is subject to Export Administration Regulations (EAR) and International Traffic in Arms Regulations (ITAR). If it's Department of Defense, it's almost certainly classified in some way.
If the DoD had their druthers, $\vec F=m\vec a$ would be classified top secret NOFORN.