Where was Haile Selassie's palace in the Ogaden Desert?

It was probably the one in Gode. More properly called a villa than a palace. But the locals referred to it as "palace" as it was still the biggest building for hundreds of kilometers around. Although some even did called that building Selassie's "Winter palace".

On 13 July 1977 Carl Gustaf von Rosen died in this 'palace' when the WSLF under Abdullahi attacked the city:

In Gode, the capital of a district of about 70,000 people, there is still a villa of the emperor Haue Selassie, reverently called palace by the population, because the emperor's house is the only modern residential building within a radius of hundreds of kilometres. The fate of the Swedish warhorse Count von Rosen, who once made a name for himself with his Biafra flights, was also completed here.

Von Rosen and an Ethiopian delegation spent the evening of 13 July in the Kaiser Villa. It was the day on which the Liberation Front launched the general attack on Gode.

"One detachment," said WSLF commander Abdullahi, "also attacked the palace." Von Rosen stayed in a room on the ground floor and fired from the window. "He was very brave," Abdullahi said, "but of course he did not succeed in taking the life of a Somali. But we were unfortunately forced to kill him."

–– „Kapitalismo ha-dhao“, Der Spiegel, 29.08.1977

Or

According to Shimelis, he was killed by an attack from Somali fighters who broke into the imperial palace in Gode, Ethiopia in 1977 along with an Ethiopian Somali official.

As we can see the expenses there were indeed substantial for an otherwise neglected backwater province, only slightly more expensive than the local school and half of what a hospital took:

_{–– United States. Joint Publications Research Service: Translations on Sub-Saharan Africa, Issues 564-585, 1967. (p 10)}

As such, the more typical dwellings in that region looked apparently more like this:

_{–– "Somali region facing food and water crisis", The New Humanitarian, 2006}

It seems doubtful that "in the desert" should mean "one single building and nothing but rocks and sand around". This Gode villa/palace would qualify for "in the desert" as Gode not only still small but it also remote and destitute:

Unfortunately, fertiliser is twice as expensive in Gode as in the capital, Addis Ababa. So is the fuel needed to pump water out of the river. The reason is that Gode is in the middle of nowhere and has no tarred roads. Its remoteness also depresses the price its people can get for their surplus crops in good years: they cannot afford to truck their produce to city markets.
_{–– "Will they ever have enough food?", Reuters/Economist, 2001.}

Some tiny and quite peripheral information describing the palace might also be found in von Rosen's biography:

Not really in the town of Gode itself, but some distance away. Built by Swedish Skanska in 1966, having thick walls, a veranda, at the time of the attack occupied by the local administrator Bellete Ergetie.
_{–– Heli von Rosen: "Carl Gustaf von Rosen: An Airborne Knight-errant", Books on Demand, 2017 (p319–320)}

It looks as if the settlement is quite a young one regarding 'proper city' features:

Gode was established in 1965 by Emperor Haile Selassie, who ordered construction of military base, well, mosque and church and laid a runway in this easternmost strip of Ethiopia.
_{–– Michal Przedlacki: "Story of Gode, artwork", 2010.}

It stands to reason that Selassie was present when "Gode Airport" was inaugurated 10 June 1966 and that he stayed overnight.

A slightly more exact location is implied in a retelling of the attack on Gode:

The Somali troops fired relentlessly at the military headquarters and the air force on their way to the palace. They killed all on their way to the ultimate goal: to capture Gode, conquer the palace and kill Adam. (Adam is the nickname of the then local governor Bellete Ergetie, LLC)
_{–– Barbro Ergetie: "Imperial Ethiopian Air Force – IEAF – In Memoriam", Tenaestelin, Medlemsblad För Svensk-Etiopiska Föreningen, Årgång 47 Nr 2 Oktober 2006, p 28. (PDF)}

Another newspaper report:

_{Stockholm (TT) Swedish flight captain Carl Gustaf von Rosen has died in Ethiopia. According to a message to the Swedish Foreign Ministry, von Rosen was killed during a guerrilla attack near the city of Gode in southeastern Ethiopia on Wednesday. Von Rosen had flown to Gode with a Swedish-registered Cessna belonging to the Swedish Journal's Ulandshjelp along with some officials from an Ethiopian relief organisation. They would meet with local administrators on a nomad resettlement project on the Wabe Shebelle River northwest of Gode.}

Attack on housing.

_{During the attack, which seems to have concentrated on the local administrator's residence, where the group spent the night, several people were killed. In addition, several people were injured, some deadly. Among the dead are the Chief Administrator of Harari Province. The local administrator of Gode, Bellete Ergetie, reportedly survived and is unharmed. He is married to a Swedish.}

_{–– "kläder till södra Afrika/ von Rosen död i Etiopien", Bygdeband – lokalhistoria pâ webben}