Great advice from @ballarinamom.
We sailed twice on Explorer as a family of 4 when the kids were younger. On both occasions we were in an oceanview. Yes, it was tight, but when it's what your budget allows you make it work.
I'm not sure if Explorer still has the showers at the entrance to the gym but if it does one of the adults could shower there to take some pressure off the bathroom in the cabin.
@cruisant, if you can possibly stretch your budget to an oceanview, it is a nicer experience than the inside simply because of having daylight and a window to look out of. But if you can't, don't sweat it; just look on your cabin as a place to sleep and shower. There are loads of places around the ship to enjoy and tons of activities and you'll have a blast regardless.