The normal procedure OP is for social services to arrange a paediatric examination in these circumstances rather than just sending you to A & E. The paediatrician then writes a report on their findings which is sent to the police and the social worker and it can be used in a criminal court if your ex is prosecuted for the assault. It would be worth double checking with the police officer/social worker concerned why they haven't done this and are just expecting you to turn up to A & E? If A & E is your only option, it would be worth checking that your daughter is being examined by a paediatrician.
Be aware that these cases can take weeks/months to resolve. Normally the police will refer the case to the CPS to see if it is in the public interest to prosecute. If he admits the hitting he may get a caution if he has no previous convictions. If he denies it, the CPS have to decide whether or not to take the case to court.
Be aware that the police have to follow a victims code of practice. As your dd is the victim and a child the police have to keep you, as her parent updated. This Victim Code of Practice contains information on on how often the police should update you on what is going on with their investigation etc.
Below are what you should expect in terms of updates from the police etc. It is taken from the Victims Code of Practice.
Right 6 - To be provided with information about the investigation and prosecution:-
6.1 You have the Right to be told by the police when key decisions on the investigation are made and, where applicable, to have the reasons explained to you within 5 working days (1 working
day under Enhanced Rights – see page 10 of this Code) of a suspect being:
§ arrested;
§ interviewed under caution;
§ released without charge; and
§ released on police bail or under investigation or if police bail conditions are changed or cancelled.
6.2 If the police decide not to investigate your case, you will be given an explanation of this decision within 5 working days (1 working day under Enhanced Rights – see page 10 of this Code). The
police will also offer you a referral to a support service.
6.3 Where the police do investigate your case, they will discuss with you how often you would like to receive updates and your preferred method of contact. You can update your preferences at any time.
6.4 The investigation and decision on whether the case should go to court can take a long time and there may be long periods between key decisions. The police will discuss with you if you would
like contact during this time and provide you with contact details if you have any questions during the investigation.
6.5 There may be times when a service provider is unable to provide you with updates and/or use your preferred method of contact, but in these instances, they will tell you why.
6.6 In some cases, the police or the Crown Prosecution Service may decide to deal with the case without taking it to court. This is called an out of court disposal. This enables the incident to be dealt with relatively quickly and may prove more effective in preventing further offences.
6.7 Where the police or the Crown Prosecution Service are considering an out of court disposal (Alternatives to prosecution, such as cautions, conditional cautions)you have the Right to be asked for your views and to have these views taken into account when a decision is made. Where this is not possible for practical reasons, the police or the Crown Prosecution Service will tell you why.
6.8 The police or the Crown Prosecution Service will take the final decision after considering the full circumstances of the offence and your views. You have the Right to be told the reasons for their
decision within 5 working days (1 working day under Enhanced Rights – see page 10 of this Code) of an out of court disposal being given to the offender.
6.9 When the police have finished their investigation, they may decide what should happen next or, for more serious crimes, pass the information to the Crown Prosecution Service, who will then
decide if there is enough evidence to take the case to court.
6.10 If the police or the Crown Prosecution Service decide not to prosecute the suspect, you have the Right to be told within 5 working days (1 working day under Enhanced Rights – see page 10 of
this Code) of the decision of:
§ the reasons for the decision;
§ how you can get further information;
§ how to seek a review and make representations under the National Police Chiefs’ Council or the Crown Prosecution Service Victims’ Right to Review scheme;32 and § how to be referred to a support service.
6.11 If you are unhappy with a police or a Crown Prosecution Service decision not to prosecute the suspect, you have the Right to ask for a review under the National Police Chiefs’ Council or Crown Prosecution Service Victims’ Right to Review schemes.
I hope this helps OP, many people don't know about it but it is worth being aware of it so you are kept informed.