im really sorry you had to see that docter, she sounds dreadfull and inexperanced. its really good news about you going to the police and yes they will make a referal to ss but seriously if its the only one thats ever been made and you are not known to them chances are you will only get a letter saying they are aware and that should another incident happen they will come to see you.
in my experance ss tend to panic much more about you staying in the suituation remaining under the same roof or not protecting yourself or the dc's and thats when they get involved and come to see you.this is because domestic violence even if your children have never been harmed/touched IS a very serious child protection issue. children love both there parents it makes it so frightoning for them if they are also scared one is going to do something bad to the other,i have lost count of the amount of kids who have said stuff like "mum thought we didnt know but we heard stuff,we were frightoned one day she wouldnt wake up" surestart and nch used to run fantastic groups for kids ss could refer your kids to simmerler.
i would really exercise extream caution about his word with regard to not causing you housing issues and going as he could change his mind at anytime all it takes is a relative/friend to validate/excuse what he did to change his mind or for you to look at him the wrong way and before you know it hes trying to make things harder for you. people often say you dont know a person untill you live with them i beg to differ and say you dont know a person untill you leave them as thats when they tend to be the nastyest.
also any formal support you get now ss/police/courts/dr's/specialist dv service will help you in the future if you ever need to prevent him harming your kids.
if you choose to stay either with him or with him in the house that is totally your choice i know i for one wouldnt judge that however you do need to know that support services could have issues regarding that but they can also help with crisis planning ect and it may very well be the can of worms you are concerned about they would have to make checks ect to make sure you and the kids are safe.
what ever you decide to do please engage with ss,they really are not in the game of children stealing the only people who really belive they are,are ones who listen to the most vile mp i have ever come across in my life and his little mouthpiece buddy who he still wont admit to being hooked up with.and people who probally should have the kids removed. mistakes do happen but they are rare (thats why they end up in the papers) if they do anything that concerns you then you can go and get legal advice. but remember there remit is that children are better left with families and a none violent parent they will allways start from that basic point, but its quite normal to be a bit nervious of them after all parenting is something most parents are sensative about as its our biggest fear and the media often play up to this as it sells papers.
you may want to know that mediation is never recamended in a dv suituation its neither safe nor workable due to the very different dynamics,even in a divorce a court has guidelines to not make mediation happen when physical dv has happened.just incase he offers to do it neither is anger management because dv is a power and control issue not a anger issue. special dv perp groups are availible but many areas only offer these via probation and they can only be accessed after a conviction (some places have private groups but not all).
i for one are very impressed with the speed you have acted to get support its brave and unusual to take the help seeking steps you have within hours of thinking about it. well done