'You don't not call me' from House of Cards

Question

'You don't not call me' from House of Cards season 1 episode 1
I found only this part on the internet.

Claire who is Frank's (Kevin Spacey) wife wanted him to call her back but he didn't.
And then when Frank is home, she says 'You don't not call me. Not when it's big'

The Conversation is below:

Frank: Claire.
Claire: You didn't call. You didn't call me, Francis. Nine hours. You don't not call me, not when it's this big.
Frank: You're right.
Claire: When have we ever avoided each other?
Frank: I wanted the solution first.
Claire: Do you have one?
Frank: Not yet.

I think it should be 'You should have called me'

My questions:
1. I would like to know what exactly 'you don't not call me' mean here.
2. Why does she use 'present tense'?
3. and the reason she is using 'double negation'

Answer 1

It's a double-negative, so just like in mathematics, 2 negatives cancel each other out.

+2 × +2 = +4 
-2 × -2 = +4

and

Don't -1 call me

means do not call

Don't -1 not -1 call me

means do not-not call me which means call me.

.

It's used often in slang form but is definitely not "proper" grammar.

Answer 2

Claire is emphatically stating a rule or expectation that has been violated. For example:

You don’t leave without locking the door!

Means: “You left without locking the door, and I’m upset.”

This is always stated in simple present tense. It can be affirmative, too.

If you stay out after ten, you call home.

This can be stated as a general rule, or emphatically in response to the rule being broken.