Joe,
You have picked the correct 3 courses.
As Sean states, it depends which way round you are playing them but if you wish to finish closer to Dublin / The North, then you have got it pretty much right.
1. Get to Belmullet for night 1. Stay in the Broadhaven Bay or The Talbot (small kitsch comfortable boutique hotel). Eat in The Talbot or in the Phoenix chinese. Have a pint at McDonnells.
2. Play 18 at Carne, have lunch in the clubhouse, drive to Enniscrone, play 18... You can go back and stay in Ballina but there's a nice wee B&B in Enniscrone owned by the ex-secretary of the club (an unassuming lovely fellow who oversaw the appointment of Donald Steel for the new holes... I can't remember his name... Jim???) with a handy and lovely pub 100m up the road...
3. Play another 18 at Enniscrone and then head to Rosses Point....
Things worthy of note: If doing the accommodation another way, I'd be tempted to stay in Rosses Point itself and not Sligo... It is a pretty old seaside village again with a nice pub or two for food and drink...
Sean's suggestion of skipping Carne is a mistake in my opinion. The dune system at Carne is unique and the course is like no other (as Jack stated). You have a feeling of remoteness like very, very few other places I know. Regardless of whether the golf strikes you as the best of the trip or not, you have a very good chance of falling in love with the place. That is why for some people it is their favourite course on earth. You have to find that out for yourself rather than take the opinion of others, no matter how good their view usually is.
Brian's suggestion of Strandhill is also a good one. Very good fun course. Then you will need to stay in Rosses Point or Sligo instead of Enniscrone.