I think your DD is mistaken about what she heard and saw, and second the advice of a pp that you need to talk to her again, explaining that this is potentially serious and you need to be clear about exactly what happened, including follow-up questions about the babysitting to try and gauge how truthful your ex has been.
Obviously, this is a situation that wouldn't have arisen if your ex had not made the error of judgement of having them all in the same room, except that the alternative - having the baby in with them and your DD in a separate room that may or may not have been near at hand - would potentially have brought its own problems too. For myself, I find your ex's account plausible, but I don't know him, and of course that doesn't mean that the way things played out was OK, because clearly it wasn't, and all parties need to understand and agree on that, and agree that nothing like it will ever happen again, and accept that this incident has done damage that it's the adults' responsibility to address.
You are your DD's advocate, but I think you also have a responsibility to act as a mediator between your DD and her father. I think a lot of the advice on this thread has focused on the drama of worst-case scenarios and has forgotten that at the heart of this situation are two people you know very well, who are both distraught. If you, in your judgement, as a person who is actually on the spot and know them both, think this is a misunderstanding that arose out of poor judgement and thoughtless behaviour, then my advice would be to take the temperature down by talking as calmly as possible to all parties until the facts are more clear, and then acting as a mediator between them until they feel able to talk calmly to each other, and hopefully move beyond this eventually, if appropriate. I think it would be best if the gf and your dh stay out of it, at least for the first conversation with your ex, as too many cooks are apt to overheat the broth ime. I think it's positive that the gf has explicitly asked permission to be there, and would be perfectly OK for you in turn to ask her not to in this first instance.
Obviously your first priority is to satisfy yourself that your ex is not an abuser, and if you cannot do so, then advice to contact the NSPCC/SS etc becomes relevant. But if you are confident he isn't and that this has in fact been a godawful fuck-up, then your next priority is to ease the distress that has arisen in your DD's relationship with him, first in the immediate term and then over the coming months.
Disclaimer for the thread police: no formal safeguarding training but many years' experience of watching runaway threads on MN cause irreversible damage in real people's lives.
