Me and my partner have been together coming up 3 years we have a daughter together and things were fine till we moved in together I keep finding messages from another girl saying things like its our little secret don't let you guard down and him replying definitely our nice little secret with kisses is he cheating as he said it was an old joke which meant a Thursday night **** and funnily enough I was away Thursday I can't stop thinking about it but don't want to ruin our relationship

Talk to him about it... Let him know how you feel. If he cares he will make some changes.

Well... first thing is don't jump to conclusions. That isn't going to make the situation better. Communication is key. Ask him about it. Don't make a big deal of it... yet. If it is something that bothers you, tell him in a calm way that even though that it is a joke between friends that it makes you uncomfortable. If he could explain the old joke or let you in on it then it may make you feel better about the situation. Or... if he could please stop this old joke because it doesn't make you feel comfortable.