Why is my dad sending sexy messages to women?

[Pr]

This is very difficult for you and it is difficult to tell you what to do for the best here. It could be a friend of your Dad's from work - you certainly might not of met everyone that your Dad knows. That said the messages, whilst certainly flirtatious do not prove that he is having an affair. I certainly wouldn't tell your mum at this stage because there may be nothing serious going on.
In my opinion, although difficult, the best thing to do is to speak to your Dad. My first thought is that as he hasn't put on sort of security on his phone to hide this stuff is that he isn't trying to hide anything. So OK he is going to be annoyed at you snooping on his phone but what is important is that you tell him how worried you are that he might leave you again. Give him a chance to explain. If you are not happy with his explanation send a message to the woman on her Facebook page. Tell her that you are your Dad's (mention his name but not yours), daughter, giving your age and that he is married and that your mother is unwell (you don't need to be specific) and ask her if she feels guilty about trying to break up a family. Leave it at that - you can be sure that whatever is going on the woman will be giving your Dad a good telling off and if she has any conscience at all will be dumping him..... and your Dad can't really get angry - especially if he was having an affair in the first place. Good luck to you and take care