Because really she just wants push Rhae out and seize power and influence for herself. That's all it's about. Alicent thinks Rhae doesn't deserve the throne because she going through her hoe phase, so she is plotting to take that shyt from her. That's why I'm team Rhae all the way.
It's even more apparent when she was yelling at her son.
"She will kill you all if you ever challenge for the throne"
"Then I won't challenge..."
"Shut the fukk up, dummy. I said you're going to be the king"
She's the one putting her children at risk. Scheming ass bitter bytch.