I think it's adorable! Love the pattern and the changes you made to be for a 2nd child. Is the batting cotton and have you washed it? When it's washed, especially if you have used cotton batting, it might lie differently. If it were me, I wouldn't take the binding off unless you really feel strongly that it's necessary. If you do decide to go that route, after checking again to see if squaring the quilt is needed, I recommend using machine binding with a flange. There are tutes all over and honestly, I think for a child's quilt it is ideal. Much faster to apply, for those of us with arthritis in our hands. And it will be sturdier, needed for those quilts that will be loved and washed a lot - which I am sure this will be.