IF you can go in October - do it.

Spring break runs from march into April, and the closer it gets to Easter, the busier it is.

The weather in October will be nearly perfect, and excepting the Columbus Day weekend crowds, it will be blissfully uncrowded (that is a relative term). You may not even need fastpasses for most rides, though you could/should get them for more popular rides.

Unless you want to pay for a VIP Guide (at $650 per hour), you really can't pay for access.

Staying at the Swan/Dophin might be your best option if you don't want to pay for a Disney hotel. You will not get all of the benefits of staying onsite, but there will be some.

If you really want the whole experience, do the disney resort thing, and save your points for another trip. It's going to cost you a whole lot more, but your kids are only 10 & 7 once, and this is the perfect age for that special trip. The next trip you can use your points