If you have access to the console, you can make the patron moon origin work with planetary diversity (at the moment, Patron Moon doesn't seem understand its custom planet types). This may work with other similar mods as well.

1. Making homeworlds work. At the moment, a capital world will *have* the patron moon as a body, but there will be nothing related to that- this is because the mod appears to not spawn the d_patronmoon deposit on planetary diversity homeworlds. To fix this, we have to add the deposit manually- open the console and enter effect add_deposit=d_patronmoon with your homeworld selected. This should solve your problem, adding a fully functional patron moon deposit in addition to the actual moon. Note that the "grow patron moon" decision actually only applies to new planets- not, as one might assume, increasing the size of an extant patron moon. If one really desires, this same method could be used as a cheat to simulate a patron moon for a world that doesn't have one.

2. Making colonies work. In my experience, the patron moon origin actually does recognize colonized Planetary Diversity worlds as worlds with no active patron moon. Still, if this doesn't work one can enter effect add_modifier=no_patronmoon to your nonfunctional colony. This will add the debuffs caused by not having a patron moon, but it'll allow you to continue the growth of our benefactor.