EMF transmission from cell phone's battery
That article you linked seems to be of an unqualified source, note that the same "Dr. Mercola" who wrote this is also active in other contra-scientific movements like "vaccines cause autism", "GMOs are evil", "flouride kills you in 1000 different ways" and similar.

Now, disregarding the opinion of this "Dr. Mercola", please consider that there are government regulations regarding ELF. Exposure to very strong electromagnetic waves can damage body tissue, but for that to occur, the waves need to be pretty strong, way stronger than your tablet/cellphone could ever generate.
For instance, in regards to induction stoves, the Swiss government recommends a distance of at least 30 cm to your cooking surface for most of the time. But keep in mind that these stoves are built to create strong electromagnetic fields, strong enough to get ferromagnetic materials hot. So basically, if the electromagnetic waves of the phone are not enough to cook inductively with (they aren't), your child should be safe with less than 30 cm of distance to the phone.

Also note the statement of the WHO that "to date, no adverse health effects have been established as being caused by mobile phone use."
So basically, your children are safe.