I can't understand why my family are pressuring me and my partner to just forget about it
they can't bear what she has become.
The claim that your partner has strangled you means that either 1) your parents believe her and should be telling you to get OUT or 2) they don't believe her but want to sweep it under the carpet.
You know, they know and your partner knows that they can't bear what is happening to your sister and that they want you to be patient and forgiving because they hope, hope, hope that she will come back to them.
But you can't go along with sucking it up. You can't trust her; you know you can't. She is terribly young but also lost right now, and that's a bad place to be trusting her with being godmother especially since she made this claims.
Unfortuantely, your parents' statement that you are using your son as a weopon is sliding heavily into manipulation. That is a choice they have made, sadly. Out of desperation and because they can't speak openly to your sister, their other daughter, but it's still manipulation. It's ruthless and unfair and it's got to hurt a lot.
I think your best bet is to say to them openly that you love them and you love your sister, but that the relationship she's in is very bad for her and you all know it. But making claims your partner is physically abusing you is something that is serious, it shows how badly astray she is, and since it didn't happen but she's still claiming it, then you need to protect yourself, your baby and your partner so no, she's not going to be godmother. It's a shame but your baby and her safety and your own happiness has to come first.
If your sister ever wants real help or to break free, you will be there for her. But you have to lead your own life and your baby and partner and happiness come first.