If it's a domestic situation, the police won't be able to give you guarantees about what will happen. Domestic incidents (which includes those with family members, rather than partner/ex-partners) will be 'only recorded on file' if there are no offences mentioned - i.e. police attend after a row but one in which no assault or damages occur. If there is any suggestion that a criminal offence has taken place, it is the Crown Prosecution Service that will make the final decision.
All that said, if it is one person's word against the other, with no witnesses or visible injuries, the likelihood is that no further action will be taken if you are not on board with a prosecution. That doesn't mean your family member wouldn't end up being arrested and interviewed, however, which is something to consider.
The options the police have to apply conditions for the family member to stay away are very reliant on you supporting a prosecution or getting a conviction, with the exception of perhaps a Domestic Violence Protection Notice/Order, but it would not be likely in this situation.
If your child was in the house at the time of the incident, a referral to SS would have to happen automatically. But I wouldn't worry about that TBH. If this is a one off and you've already decided the family member is no longer welcome at your house, SS will see that you have taken positive steps to safeguard your children and they're more likely to ask how they can help than they are to criticise you. If this is an isolated incident, they won't be opening up a file for you and seeking to remove your children. You might get a phone call or a quick visit and that would be that.
Many victims worry about the consequences of reporting, and TBH some of those concerns are valid. The support for victims simply isn't there as much as it should be. Doing the right thing can often lead to a lot of aggro for a victim that's almost as bad as what they've reported. However, unless you are sure this is a one off, reporting is the best choice. If this family member is likely to cause future problems, you will need to use the system to protect yourself and you cannot do that unless you can prove an ongoing history - reported incidents, even ones that don't result in any criminal proceedings, at least document every occurrence and show you're not making stuff up retrospectively.
Good luck. 