I have a kindle fire and really like it. I've found it pretty easy to use, but I have no real experience with other tablets, so can't say how it compares in terms of user friendliness. Battery life will depend on what you're doing. It's good if you're reading books, but some of the apps we have eat battery very quickly.
We have it set up with different profiles for me and the DC. We've set it so internet and downloading apps is only available from my profile, which is password protected, so that DC can't get unsupervised access to the internet or YouTube when using the kindle fire.
The profiles we've set up for the DC only have apps on that we've selected as being suitable. You can set time limits up so that the DCs can only access their profiles at set times of the day (e.g. not after 8pm or before 8am), and you can set limits so that DCs profile can only be accessed for a total length of time in a day (e.g. 1 hour on the kindle fire a day).
No idea about Animal Jam or Minecraft though.