Now I'm no expert in Google Earth nor the .kml file that it uses, which my answer in a moment address thus i might be unaware of a possible solution, but I'd like to help you in lack of other responses.
It's probably because Google Earth can't save the different EPSG's for both planets, in the same file. That's problematic in many other filetypes for GIS systems too. Thus you will need to save Earth data in one set of files, and Mars data in another - sadly.
The explanation: A big issue with all precision task on maps, be that analogue or digital, is how to handle the the fact that spherical balls such as the Earth and Mars,is drawn on a flat paper or presented in a flat screen. In the analogue days this was "categorised" as a Datum, that explained how each maps was projected to "2D". And the way you reference coordinates have traditionally been done in degrees, such as 3 degrees 45 minutes and 20 second (3*45'20''). Each of these datums have their own limitations, and are often regional to be more precise in that region, such as UTM 29 North, which i choose as an example, because the UTM zone comes from a highly popular alternative to degrees: how many metres you are north/south of the equator and how far east/west you are from London with the zero line through there, just as the degrees. Degrees are divisible by 60, so one minute is 60 seconds, metres are in 10's, or 100's or 1000's (i.e. kilometre) - much more intuitive to use when we have a 10 base number system.
So in all GIS work, including Google Earth, the system uses an EPSG number, stating which Datum etc., to use. And i guess Google Earth just uses a single one for each planet, and don't bother people about which one to use.
I allowed myself a quick look at your profile, and saw that you'd tagged QGIS as well. If you open QGIS, you'll see this EPSG number in the lower right corner as a standard, and often when opening data (with unknown EPSG) QGIS will ask you to state it, in the screen that also shows a red square over the world, presenting where the EPSG is suitable - this is was Google Earth probably lacks, and most certainly causes malfunctions between planes.