If you are " only good for babysitting" then she is obviously not worried at all about leaving you in charge of her children. X
You say she txts or e-mails you afterwards and apologises, so she knows that she has hurt and upset you,
I would be more worried that she is suffering from some sort of post natal depression, or worrying herself that she is not coping well.
Its a hard one, but maybe you could broach the subject when she is in a good mood, and just let her know that you are there for her, and if you can help in any way, even by just giving her a break then you are willing and able.
Good luck. X