Your best bet is to try to phone in and get a sympathetic agent to waive the fees and seat you. But it's entirely discretionary, you have no right to claim these seats, it's just if they're feeling nice or generous. Or try to get some seats when you check in when some of them are released, but there’s no guarantee to this strategy.
Once you get on the plane, it's unlikely you'll get people to move. Travel blogs are full of complaints from single travelers who paid the US$100+ to get an aisle seat, who are then asked by families to move to an aisle seat so that they can sit together.
There is unanimity that this is not a fair request unless they are being moved to an equivalent aisle seat or bumped up in service class (from an aisle in economy to a middle seat in business or economy plus), or that they are being paid a cash amount that satisfies them (not necessarily the cash amount they paid for the initial aisle seat placement).
Indeed, cabin attendants are loathe to force anyone to move unless there is an equivalent or better seat. So the family only has the power of pleading. And people are increasingly not moving, because they paid that $100 for that aisle seat.
The reality is that aisle seats are a desirable "product" and the airline is free (absent legislation passed prohibiting it; a moral outcry from its customers; or customers shifting to companies without these policies) to price its product in a way that gets maximal profit. Unbundling services to reduce the base cost is now common amongst carriers and it's what we get by sorting by base price.
I really hate paying the $100 for my own singleton travel but I do so (or fly on an airline or in a class that allows for aisle seating). May I ask -- in all bluntness -- why you feel entitled to get a product for free that others have to pay for? If I have wide shoulders or long legs that make sitting in middle-seats uncomfortable, should I get an aisle seat for free? Should couples or business travelers who want to sit together also be able to petition for a waiver of the aisle-seat charge?
The one exception I could see would be a waiver for children under 12 to sit next to an adult but that only applies to one of your four children.