Well, if he's calling you because he's desperate to drink, then I would think that you would rather have him call you than not. You obviously don't want him drinking around your daughter. In this instance I would say protecting your daughter trumps any concerns about your enabling his drinking. If his failure to abide by the visitation schedule is creating problems, then you probably need a different schedule. If you can't work it out between the two of you, you may have to go back into court and have the judge decide.
I think I'd keep up communication for now, if only to monitor what is going on with him.