Hi Op, some of the advice you have received is spot on.
I work at a primary school, so I can also confirm that it doesn't matter whether an incident happened after school hours or not. If it is a safeguarding concern (and based on what you have said it definitely is), then the school has a duty to investigate and do the relevant referrals. If they don't, they are in breach of duty.
Your school must have a safeguarding policy (check on their website, or ask for a copy at the school office), and in the policy you will see who is the Designated Safeguarding Lead (at a primary school it is usually the Head teacher). You can follow the procedure for reporting an incident. It will have to be in written so they have a record (explain everything in detail including the day and time), then date it and sign it. The school will have to start their part and deal with it. They should inform you what action they have taken, but they won't be able to tell you more than that due to data protection.
If you feel you cannot report the concerns to the Designated Safeguarding Lead or you have but you are still worried about the safety of the child you must still take action - report to First Response (children's social services).
And do not talk with the teacher again (unless she is the DSL, although that would be worrying), because the advice she gave you was wrong. You should not speak to the child's mother about your concerns.
If you see the girl is on her own in the park again, or locked out of her house and you are worried and don't want to leave her on her own, I agree with other posters that the best thing to do in this case would be contacting the police.