Turkish Airlines and AnadoluJet Flight Rescheduling Issue

My Adana-Beirut flight scheduled for March 4th with AnadoluJet was postponed to March 7th. However, I had already booked a Van-Adana flight with Pegasus for the same day. Now, they are telling me that the two companies are different. The only way for me to travel from Van to Adana is with Pegasus; otherwise, I need to make an extra stopover in Ankara with AnadoluJet, which is unreasonable. I will be inconvenienced with my baby. I want to add that you were the ones who changed the flight. Normally, when such changes occur, even a hotel is provided. I have communicated this issue to the company employees, but they told me it was a 'last-minute inconvenience.' There is no such thing as a last-minute or ten-minute inconvenience. AnadoluJet should also cover the cost of my Pegasus flight. Because of you, I had to buy a more expensive ticket, and my plans were disrupted. You are responsible for me having to fly at midnight with my baby.