Should I break up with him?

Anna
So I met my boyfriend online (its long distance) last year we've been together for 16 months now and just recently he's been disappearing on his days off. He doesn't bother to call text or Skype me letting me know he's ok. I have access to his Facebook because he said he wants me to trust him but I messaged his ex on his Facebook because he's been spending more time with their little girl recently, (I have no problem with that) but I asked her to tell him to come home when he comes by and everything is over for the day...so she tells me yeah Ill wake him up and tell him...he's been sleeping at her house all this time and hasn't told me:/ even though his ex says he's sleeping on the couch (she hates me and would do anything to ruin our relationship btw) I'm still not comfortable with it and that he lied to me about it...should I break up with him or try to work it out? I honestly love him but I don't know what to do anymore.