Ash:
1. I would actually favour the September date, which might be a bit counter-intuitive. The weather is unpredictable at any time, and perhaps even a bit drier in September as has been pointed out above. The main advantage to late September would be that the late September/first ten days of October should see a reduction in crowds.
2. Re accomodation. I believe you have said you are on a budget. In that case, for Portmarnock, I would go with a B&B in Dublin, or perhaps in Howth depending on whether it is important to you to be close to the nightlife, apres golf. There are lots to choose from, but try for instance Howth View in Portmarnock. If you prefer Dublin there is a wealth of choice and the only real parameter is to be sure to stay on the north side of the city (for Portmarnock at least).
For RCD, we have always enjoyed The Briers Guesthouse. Portrush/Portballintrae has multiple options, and again, if on a budget I would simply book into a B&B. By early October the crowds will likely be subsiding and you should have several options. Lahinch also has loads of (relatively) inexpensive guesthouses, such as the Greenbrier Inn. Ballybunion has perhaps fewer per number of visitors; for budget options we have liked Teach de Broc or The Tides. Finally, in Waterville the Butler Arms Hotel is a great splurge if you can afford it; if not there are a few B&Bs very close to the links. Be sure to go to the bar at the Bulter Arms in any event to visit the place of Payne Stewart's exploits on the piano and behind the bar shortly before his untimely passing.
I hope that helps.