Should I arrest my blackmailers or pay them?

From an Anonymous Reader:

I am a 54 year old woman who for the first time in my adult life got into a physical fight with a 21 year old girl. She slapped, kicked and even tore my blouse in front of my pregnant daughter. I am writing this letter with the consent of my daughter. 

I am a lecturer in a Christian university here in the east and I go to Lagos every weekend to see my family. Been married for over 30yrs and I have daughter. 

Ok, My daughter phoned me one day and told me about this 21 year old girl  her father has rented a house  and have bought her car for. She also said she suspected they have a baby together  because she checked this girl on Internet and she puts pictures of a baby up. Continue...

So after further investigation we found out where she lived and one good sunday morning after church we went there. I saw her, very pretty  young girl. She even looked younger than 21. Calmly  I started to talk to her, asking her questions like my own daughter and she answered respectfully.  She was calm until her mother came out and ask who we were. 

And then you know daughters now. My daughter challenged the woman Before we knew what was happening,  this little girl just changed , as if she was charmed and started to curse my daughter She and my daughter started exchanging words and my daughter called her son a bastard. Dat was all. This girl rushed gave my 30 year old pregnant daughter a slap she ll never forget in a hurry. 

Being a mother I tried to defend my daughter who has started to shout. My intension wasn't to fight . But I couldn't help when I realized we were being attacked. This girl slapped me n tore my blouse, while  her brother or boyfriend was busy filming everything  with his phone. 

Since then someone has been blackmailing me with the video of me fighting with my breasts hanging out, threatened to put it online if I don't pay certain amount. The question is should I pay or just face the humiliation. I know my job is on the line. My husband that caused all these is away in the US but has given me his consent to arrest her and her friends. 

I'm soon to be a grand mother. Should I arrest these people and risk everything or just pay and leave the rest to God.