Ok, if L says not to move out, then staying for daughter is most important.
How do you handle those conversations? First of all, don't have them. Validate her feelings and don't drag out the conversation. I suggest you spend as much time away from the house as possible, take your D places, and when she's not around, just go out.
M - 9 1/2 years 5/5/16 - Bomb drop - 3 week EA 10/31/16 - We sold house 01/10/18 - D Finalized