That's why I think she is a bad mother where Kristina is concerned. Instead of holding her accountable and treating her like an adult--she babies and placates her. Alexis agreed with Ava months ago, that Kristina's fall was a horrible accident. But not only has she not said that to her woman-child, she remains silent as she rants about Ava and calls Molly & TJ's daughter Adela. The baby's name was Irene.
I know that Alexis loves all of her children but she absolutely doesn't treat them the same way. She shows clear favoritism to Kristina because she needs her more. She said those very words to Molly. Alexis hired Diane and then proceeded to do the exact opposite of everything she recommended was necessary to lessen the fallout. She knows that Kristina planned to kill Ava but nearly killed Ric and Liz but she is in protective mode.
That being said, the other reason Alexis hasn't said anything and it's a big one--she knows Kristina will crack like an egg. If she were to learn that Ava has proof, she would do something reckless because she is a the epitome of a lose cannon, wrapped in a basket case. Kristina would either confront Ava or race to the police station and spill her guts. The latter being honorable. Alexis knows her daughter would handle it in the worst way possible and thus she has decided to protect her from that intel.