For others who are stuck with this too. I started playing today and Jamgill's suggestion worked (after a couple of tries).
Go to launch pad, click "run test" on the booster and it should launch. Once you're up to 47000 meters (or whatever altitude u need), click the booster and select "run test" once again. Only after that, u can decouple and land! Finnicky and unneeded frustration, but at least it eventually worked for me.