I don't have kids, so take my opinion with a grain of salt. I think you are comparing apples and oranges, though. I love love love the Swan and Dolphin because it offers luxurious digs in walking distance to both Hollywood Studios and Epcot. But theming is not hugely important to me - I'd rather have the Starwood heavenly beds than the Disney theming. On the other hand, you can't beat that feeling of immersion in Disney details at the Disney owned properties.
I ran a couple searches through my usual discount channels - I always book Disney resorts through Orbitz stacked with an Orbitz promo code. If you are interested in pursuing the savings, it's fully refundable up to 5 days before travel and works seamlessly with
MDE. You will need to wait for Disney resorts to be loaded into Orbitz for that time (if they aren't already, I did not check) and be prepared to cancel and rebook if a discount comes out, or simply wait for your desired discount before booking. For the same weekend this year, with a 15% 2 night minimum Orbitz promo code, they have POP $118 per night, they have Caribbean beach for $176 and Port Orleans Riverside for $187 per night. I have not stayed at Caribbean beach but Port Orleans is almost as nice as the Swan/Dolphin in my opinion, and parking is included in the rates I searched above.
For the Swan/Dolphin, I always book through LMTclub.com. I found a promo somewhere that waived the "annual fee" for this website - they always have the lowest rates for Swan/Dolphin when I search and (secret tip, I'm wary to even share in case they stop doing this) the resort fee has always been waived when I book through them. It doesn't say it at booking but it shows up to the front desk person that way. For the same weekend you're looking at in 2015, lmtclub has the Dolphin for $170 and the Swan for $192.
Due to the location alone, I'd go for the Swan/Dolphin. They share the Disney resort benefits, and I prefer the decor and bedding. Again, I don't think you can adequately compare these rooms to value resort room amenities and accommodations. To me, the Swan/Dolphin are lightly themed deluxe resorts at a moderate price. As far as magic, I love the restaurant choices nearby (world showcase is not far) and it doesn't get much cooler for kids to be able to take a boat to and from your resort! I see the magic there, but I can understand how there is different appeal in different resorts.
Regarding magic bands, I'd pay the $12 per person and not let that influence my decision on the resort. I certainly understand keeping a budget but if you decide that the Swan or Dolphin works better for your family, the magic bands are really not that expensive (but I do think they are worth the money versus using RFID cards).
If you have questions about using the discount websites feel free to PM me and I will help you out as best as I can!