He would stay at the Neues Palais. It was not erected with hessian money but exculsively out of his parents own property (predom. by Princess Alice's dowry). For that reason it was not among the expropriatetd houses and as a matter of fact remained with the family until 1941 when Prince Ludwig sold it and - thank God - brought the collections of art to Wolfsgarten.
My own grandmother would be invited by the grand ducal couple to a ball in the NP in 1931 and her father would get a postcard by Count Hardenberg asking him for a visit there in 1921. The Vermögensverwaltung remained there as well.
Kranichstein - by the way - remained with the family as well until the Prince sold it to the Jägervereinigung in (I think) 1951
That's interesting - and strange! The New Palace may have been built with private money, instead of money of the state of Hesse, but the 1919 agreement states that, in principle,
all land and buildings that the Grand Duke used or which he had the usufruct of property of were expropriated, insofar as they belonged to the family estate of the grand-ducal house ("
Familieneigentum des Grossherzoglichen Hauses"), with the exception of some specified properties. Wherever the money initially had come from, it seems unlikely that the New Palace was not considered as part of this family estate. I checked the 1919 and 1930 agreements to see how it was possible that the 1919 agreement suggested the New Palace was expropriated, yet the palace was still used by the Grand Duke in 1921 and 1931. The documents aren't very clear, in my opinion. The 1919 agreement provided in a transition period in which Ernst Ludwig could clear the properties that had been expropriated. It seems likely that these provisions were implemented rather flexibly, as the 1930 agreement confirmed that ownership of any real estate belonging to the "Familieneigentum des Grossherzoglichen Hauses" had been transferred to the state of Hesse, but that - as I understand it - Ernst Ludwig was allowed to use these properties as long as necessary to allow a smooth transition for staff members and as long as the state did not need these properties for other purposes. It seems to have been a most generous agreement that left Ernst Ludwig little to complain about.
The situation with regard to Kranichstein wasn't entirely straightforward. The walled section of the Kranichstein estate was listed in the 1919 agreement as one of the properties excluded from the expropriation, insofar as that the
Hofmarschallamt was allowed to 'lease' it. Sounds like a strange construction. Full ownership was returned only by the 1930 agreement, which explains why Prince Ludwig was able to sell it in 1951.