They will be fine and can probably get by with the shorter/cheaper Big Box Store or Amazon hammocks. Be sure to have some sag in your setup (ends hung at a distance about 83% of the physical hammock length apart). Have them lie a bit diagonal (head left, feet right, or reversed). Suspend the hammock at a height so that when they sit up, their feet are on the ground - like sitting in a chair. Let them know the hammock is for hanging out, not for bouncing.
Understand that they may find it fun for one to hang on, inside the hammock, while the other rolls them up like a burrito, So be especially careful to set up with nothing hard/sharp/pointy under the hammock. If they want to be next to each other, they can share two trees. Rig the hammocks so the suspension of one comes off the tree's left side and the other comes off the tree's right side.
REI is currently having a 20% off sale, and the Hennessey Explorer model is often the "gateway drug" for a hammock camper. But you should first ascertain if your kids prefer that. There's something about a Tent that is appealing - until crawling around on the ground is not.
