Well, the PLO sent fighters to help Amin. What if after Black September the Palestinians established a significant base there with USSR aid for safety from the Israelis? This would allow them to train, organize, and equip with far fewer troubles. After units are fully trained in Africa, they are redeployed to the Middle East. PLO hostages, kidnapping, ransoms, money laundering, etc. are also run through Uganda. IATL the Middle East is only for fighting, not where the PLO is headquartered or trained.
When the Uganda_Tanzania War breaks out eight years after Black September, the Palestinians have 5,000-10,000 trained men there with heavy weapons, some armor, and maybe even some jets and helicopters. Sort of similar to OTL Hezbollah or ZIPRA during the Rhodesian Bush War in being a non-state organization that has capabilities that look similar to a small state actor. These forces are deployed because Arafat finds Uganda useful as a staging area and doesn't want to lose it. Seeing his Arab brothers going in whole hog convinces Gaddafi to go all out and with Soviet logistical support he deploys several thousand more soldiers there than he did IOTL.
This all either allows Uganda to take the Kagera region (part of it or the whole thing) or at least makes thing bloody enough that Nyerere contents himself with driving them out of Tanzania and doesn't invade Uganda itself to overthrow Amin.