For your apple devices, you'll have to use the iTunes Store. For ds we pick and choose specific episodes, often about £1.49 each, but sometimes worth buying the season if there are enough she likes.
We have also downloaded a bunch of stuff from DVDs onto our computer and transferred them onto the iPad so we don't need to pay for things we already have on DVD.
You can also download episodes from the Sky Go and BBC Iplayer apps so you don't have to use up your allowance there. Quite often you can download them for a month, but will delete 48 hours after you start watching the episode. Depending on your home internet provider you may be able to log into wifi while you are out and about, and lots of places have free wifi you can use (although this may involve signing up for company newsletters to your emails, damn you Dobbies!).
Your iPhone 6 can also create an Internet hotspot for your tablet while you are out if you really need it to you can do this in Settings and it gives you a passcode to use on your tablet. We have a pile of apps MiniAsh can use when we need as well in case he gets bored of cartoons, he likes the Lego Duplo and CBeebies ones, some free art and music ones as well, sure you've found some of those yourself!
I don't have an Amazon device so can't help you there, sorry. Sure someone will come along who does. Hope this helps!
