General aviation corporate jet Captain reported descending to avoid Class B airspace on a VFR reposition flight due; ATC issued a heading toward a ground obstacle. The controller issued a revised heading and the Captain climber the aircraft to avoid the obstacle.

Narrative

We had dropped our passengers at LXT and were on a VFR reposition flight to MKC. We called the MKC tower on the left downwind exit of the pattern from LXT and indicated we had the ATIS and were inbound to land.The tower initially told us to head toward the airport but then after a short bit changed and asked us to fly north and maintain current altitude. We did this; but it put is pointed directly as the MCI class B airspace. The controller was busy and we were unable to inquire about the vector. When it was obvious he had lost SA; I descended the aircraft to 2500 to stay below the Class B at 3000' MSL. As we were about a mile or two under the Bravo; a different controller (the trainer??) instructed us to reverse course right turn and head south. We complied with that instruction; still at 2500' MSL.However again it seemed as the trainee controller was not keeping up and this had us pointed at some antenna. After we cleared the Bravo above; I climbed the jet back to about 3500'; and just as we started up the controller seemed to realize the issue and started to issue an altitude change; but I think saw the climb and stopped mid sentence.After a bit the other controller (trainer again??) told us to fly west and enter the downwind. After that everything was normal.I understand the airport got busy and the controller trainee seemed to not keep up; but the instructions given to us would have resulted in an airspace violation or close to an antenna. It would have been better for all involved I think if he had just said 'remain outside class D and I'll call you'. As it was I was guessing what to do; but didn't want to get a phone number to call so we adapted as needed to stay out of the Bravo and avoid obstacles.