Even though 1.5 years old is young, given the situation, I would find daycare for the boy. There are a lot of resources for that - your sister needs to go to the Social Services agency of your county and ask for childcare resources, explaining that the situation is urgent. A qualified, state-tested childcare provider will be far better for the baby presently than either the abusive dad or the depressed and desperate mom. It can be a safe haven for him, and I mean it literally and not figuratively. Hopefully the immigration will follow through and have him deported. It is highly unlikely that your sister will get any financial support out of him when he is in South America, but still, both for the sake of her future ability to remarry legally and for the sake of ensuring that he stays out of the States, she needs to go to Legal Aid and file for divorce ASAP. If the court orders him to pay support and he leaves the country and accumulates arrears in support, it will effectively block him from re-entering the US (if a felony conviction were not enough...).

If your mom can help stay with the boy for a bit, that would be very helpful too, but under your sister's circumstances, a routine, well established child care she can rely on would be best. Then grandma can help out during weekends.

You did a fantastic job pointing out to her that had he not had prior convictions which were not associated with your sister, this one would have been the first and would not have gotten him deported. Hopefully she will hear your logic on this. You did everything correctly - there was no better way to deal with it. It is tough, but every step you took was appropriate and much needed.