Pegasus Airlines complaint: Missed flight/didn’t allow for boarding

My daughter on 19th November morning at 00.30 got 2 boarding passes at Dubai airport to fly St. Petersburg , Russia. Dubai to Istanbul at 3.20 am and Istanbul to St. Petersburg flight which was at 9.45 am departure respectively. She flied from Dubai to Istanbul and reached there at 7.30 am. Then she went through immigration control where she lost almost 1.30 hrs due to long que and reached at boarding gate 30 minutes before departure of flight. But they didn’t allow her for boarding and told boarding closed. She lost her flight and they also left her baggage. Later when she asked airlines what to do now, they told they will accommodate some next flight. One woman from airlines kept her passport and boarding pass whole day to send her on next flight and told she can’t buy ticket. Then in evening told buy a new ticket. I bought new ticket for her via different countries because direct flights already left day time. Now Pegasus will tell what I should do? Ask for compensation from them or sue to Pegasus due to her emotional stress?