just had a 2016 30ds (18,000 btu atwood) out in mid 90 heat with high humidity. ran air 24 hrs a day ( got ahead and stayed ahead of the game). installed reflectix in front window against glass, then set shade down. installed reflectix on back window, then shade down. installed 3 camco vent insulators. set thermostat to 69 with fan ON all the time mostly on LOW,and once at medium. everything stayed cool. If you need to, open quick air dump vents right at ac and DO NOT go thru ducts as that restricts air flow. You should be able to keep the bedroom door open.
One final thing, the RV was east to west lengthwise, things may have been different if the RV was north to south.
the main thing here is you mentioned 15,000 btu, not 18,000 btu.