I understand that you may have changed certain details to protect your rl identity but I'm sure you can appreciate that, given the conflicting information that you've put out, it's difficult for anyone to advise you appropriately.
The source of your angst has variously been described as your dp, your fiance, and your dh. You've said you left your abusive exh for him and at one point mentioned that you needed to get a divorce - which prompted some query as to whether you wanted to divorce your exh or the man you were claiming as your current dh.
You've said you've financially supported him for the past 3 years (effectively since you met him), and you've also said he's worked 38 hr weeks and plays drums in a band - the latter being a source of tension when he told you he intended to give up his one day a week electrical course in order to try and make it as a pro.
I seem to recall you've also said that you live together but he doesn't stay overnight in your home because it would adversely affect your benefits. If that's the case, seeing him every day now you're having time apart to work on your individual issues wouldn't seem to be any great departure from what has been the norm.
You say he hasn't punched you but on a previous occasion - in your own words - "he hurled abuse, slammed doors, tried to push me down the stairs, elbowed me in the ribs, shoved me, told me it was over and left with his stuff"
This led to your dd1 waking up and saying "Why are you crying, Mummy? Has Daddy hit you again?" which would seem to indicate that him being violent towards you is something she'd witnessed before. On that particular occasion you were advised to contact Women's Aid.
After this last tempestuous bust up, you've said that 'The children are distraught with the shouting'.
This time for the sake of your dds, I again suggest that you ask your GP for a referral for assessment for pyschotherapy to enable you to break your destructive pattern of entering into relationships with men who have no respect for you, and who certainly don't love you in the way that you deserve to be loved.
Sadly you still appear to be intent on playing 'happy families' with this self-absorbed manchild and, if you are so far removed from reality as to believe that falsifying your dd1's birth certificate is of no consequence, I have little confidence that you will see that remaining in this violent and abusive relationship is not conducive to the welfare and wellbeing of both of your dds.