Should i look after my sisters baby?

Ok here is the story my sister is not coping well at being a first time mom at all. She is 19 and had her baby 2weeks ago since the birth the baby is a sensitive baby, she likes things quiet and likes to be held. The problem is the baby now has colic and lastnight she kept on giving the baby to my mom as she say's she can't cope. My mom and her partner live with her but her partner is useless. The other night she went into my mom at 4am as she couldn't get her back to sleep so she let my mom do it for her. Since having the baby she moaned she was tiered so i looked after her baby and my own 2 children who are 2yrs old and 4weeks old while she went to sleep, i let her sleep from 7pm till 12 and then she went home with the baby. Since this i have done this another 2 times and it's quiet hard as i have my own newborn and a toddler and then her baby that has colic. The problem is i think she may be postnantal as she has asked my mom to HAVE the baby and my mom has said no and things calmed down i know she didn't mean it as i know she loves her baby she is just finding it hard to cope. She shouts at me and my mom all of the time even though we are just trying to help her. All she wants to do is sit on the sofa as she is and was before she had a baby a very lazy person. My mom makes her bottles and washes her and her bf clothes and as she hasn't applied for her money yet my mom also has had to buy the babies formula and nappies and i think this is wrong. I know that she needs to step up and be a mother but my concern is more for the baby than for her as if she is tierd and is angry all of the time then her baby will sense this and the poor thing has colic and needs someone patient to care for her. I was wondering what you think i should do. Should i offer to have the baby for a while? or Should i let her deal with her on her own?