I was never able to get Sims 3 to run properly with Island Paradise, it would crash and get more buggy than normal every time. As far as I could tell, when living on the mystery island, services don't work at all. You can try to evict the household and then put them back again. I have found that this helps sometimes. Be aware though, you will lose any wishes you have, so if you are waiting to fulfill that big wish to get married, wait till you do that and then evict.
*Evicting is done from the edit world area
I hope this helps!