October is Mallorcas wettest month, and you'll only get around 3 hours of sun a day. Temp will be about 19 degrees - so not great.
Personally, I don't see the point in spending all that money to go somewhere not much better than the UK.
What about Cyprus? You still run the risk of some light showers, but overall it'll be much warmer, with average highs of 29 degrees.
Paphos is lovely, and there's so much to see and do. If you're going for a week then I'd spend 4 days in the hotel/resort and 3 days hiring a car and taking in all the amazing sights that it has to offer.
If you want to go down the holiday village route, then First Choice will probably be your best bet, but they are incredibly overpriced and with being 'all inclusive' you kind of feel like you're stuck to the resort.
Personally, with children of that age, I would look at going half board. All Inclusive, in my opinion, is only really worthwhile if you're planning on going on holiday and making full use of the "free" bar - which I'm assuming is not something you'd do with young children! :-) It also means you don't have to stay at the resort/hotel all day and are free to wander around, picking up lunch on your travels, and heading back to your hotel for dinner.