In my practice, I do a quite a bit of work with Cleft lip/palate patients. As the restoring dentist I coordinate the treatment with the oral surgeon and or plastic surgeon. In your case, it seems that taking care of the infected teeth or gums should come first as this can interfere with surgical results. After this, consults with a dentist who handles these cases is in line. This dentist should arrange consult with the appropriate surgeon. This is to ensure that the gameplan or blueprint is completed and doable.
In a lot of cases, we build the teeth and gums to help support the lip. So sometimes some form of temporary teeth are used to allow the surgeon an idea of what needs to be done. These temporary teeth can then be altered if necessary to help compensate for support that could not be achieved with the surgery.
There are not a lot of dentists who handle this type of work so you may have to reverse this consultation protocol I mentioned and see the surgeon first and ask for a dental referral. By all means have a game plan on both ends before anything is done.
Finally be hopeful as I have been involved in some really bad cases and the results have changed their lives!