She's probably got some ring ins looking her kids, people she doesn't trust. Her children safety could be compromised because your a selfish arsehat. You know nothing about her life stop being such a twat it's ugly.

She prob had to beg for babysitting in the end

Some of you people need to get a life. Maybe she didn’t want to work because it was stressful managing 3 baby sitters.

Probably just didn't want to work. So she tried the most obvious excuse ”babysitter”

Let it go

Confront her for what? Everything she wrote could have been true for her. She may not have had easy access to babysitters but had to in the end employ some or ask acquaintances that she didn't feel comfortable asking until she was put in the position to have to.
And she probably is stressed and finding babysitters was an extra stress. Or maybe she just wanted to be home with her kids because that's where she feels happy after being stressed.
Who knows.
She could have written a text thinking it was clear what she meant but you've taken it a different way. That's the thing about texts, it's very easy to not really understand what that person 100% meant.
She asked you and you said no. Which is your right.
But I dont see what calling her a liar will achieve unless this is the last of many obvious events of catching her lying.

Keep a record of everything she says to you. Request she text rather than ring so you have a written record and keep your responses polite and short - imagine the conversation is something you will be showing your boss when the trouble starts.