Can I get all the shows where the male lead falls for the female lead who has a child. Eventually the ex comes back and causes problems for them. The child takes to the male lead and he becomes their father over the real father.

None of these fit exactly, but:

  • Ms. Perfect - Sung Joon's character is arguably the SL. He falls for the FL, who gets a divorce during the course of the drama. Her ex-husband continues to have a relationship with the kids, but the SL ends up with the FL and they raise they kids.
  • Marriage Contract - the bio dad has passed away, so he doesn't come back to cause problems (his mum sort of does though)
  • Madame Antoine - the FL is divorced, has a kid, and ends up with the ML, but her daughter lives abroad and moves in with her ex-husband

Edit: also these are historical dramas with very different dynamics, but maybe the King's Woman and arguably Empress Ki

  • Oh My Lady - very adorable dynamic between the daughter and the male lead
  • Good Job, Good Job - though at the start ot was never revealed that she is the kids mom.
  • A Thousand Kisses - definite the drama you are looking for, but thwre are part that were just plane stupid and irritating
  • Fierce Wife - a must watch for dramas with divorcee with child. Though it doesnt fit the latter part of your discription

Thank You --- It has exactly everything you asked for ...  and it is very very good.