I agree with putting the sim in another phone and putting it in a drawer switched off (preferably one of your drawers so your DD doesn't even get to see it). This will allow the dreadful family to dig their own grave as the abusive messages will continue.
Absolutely print out the messages to date and provide them to SS.
Part of me agrees with informing the police, as this is definitely harassment, however I would be a bit concerned about upping the ante and the potential consequences. If SS have logged the time of the phonecall, there are ways that the police can identify the number that made the call, even if it was anonymous of your DD does decide to report it as harassment. Having the crime number of harassment may help to ward off any future attempts by the father to gain PR.
As a cautionary tale, my friend got pregnant to a guy. He was awful - a white supremicist, violent to her, and bi-polar. She ended the (brief) relationship before her baby was born. She didn't put him on the birth certificate.
He made disclosures to medical staff that he intended to kill her and the baby, and there was a SS recommendation that he should never have access to the baby unsupervised. Despite all this, when he went to court to gain parental responsibility, the court granted it. Thankfully he lost interest when he had to fund taxis for a family member to supervise contact at a contact centre, and the child didn't instantly run into his arms (I'm still so proud of her that even at such a tiny age she had the ability to display utter disdain for this bloke).
I'm not trying to scaremonger. The stress that my friend went through was awful. He got PR, despite all of the indications to the contrary. So although reporting this to the police as harassment may be a red rag to a bull, it might be worth going through that to get a strong evidential base should the father ever change his mind about contact.
YY to also locking down all social media, priming any mutual friends (hopefully there are none), getting a new number.
I think it is lovely that your circumstances are such that you have a granny flat where your DD and her baby can have their own space with you onsite. Win win win all round.