It isn't because the op is a female I'm saying this. But she hasn't killed or hurt anyone. It's not a good thing to do but it's not like she's stolen from a vulnerable person.
She's admitted fault and is trying to put it right. And they seem truly remorseful.
I see no point in kicking op further when they are clearly down.
They were obviously in mental distress and it can make people act out in all kinds of ways.
Op as to how you tell your children, I'd maybe get involved with a gambling charity. They should have advice.
It was very wrong of you to do what you did but you know that and don't need a pile on.
Mumsnet is very black and white thinking sometimes. Try get some counselling too if the gambling charity offer it, I think you could do with it.
Maybe ask social services for some help as well.
I doubt you'll get sent to prison, especially if there is no one else to look after your children. Just learn from this, seek support when your mental health is going down the drain and keep on your meds.
Some people do have addictive personalities, just be mindful of that when you are going through your next bout of stress. The brain likes to clasp onto things it can control when you feel out of control. But unfortunately the gambling got out of control too.
Have a go at practicing mindfulness. Also try youtube for meditation videos. Try pura rasa, she's very soothing. This should help calm the turmoil.
I wish you the very best, I truly believe you are remorseful.