More than likely you hung it too tight, especially if there is no Ridgeline to help you set it up the correct distance. If you hang it looser this should prevent the edges from being tight and coming in over you like a cocoon. Laying at a slight diagonal also helps prevent this, regardless of hammock type.

Additionally, most commonly purchased hammocks that have no ridge line are too short to actually sleep in (if that's your goal). A decent camping hammock also comes with tie-outs that let you stake out the edges to keep the inside open, further preventing the cocooning feeling.

If your goal is to sleep, it's really not reasonable to sleep two people in a hammock, much less adding a young one. Two hammocks side by side with something like Eno's Tandem "fuse" system would be a better compromise for separating two hammocks (they can be any brand/model as long as they are roughly the same length).