This is going to sound odd, but it has worked very well for me on more than one occasion.

Anway, have your child sit so far back on the toilet seat that s/he can touch the back of the toilet bowl ring with their tailbone. The way I am guessing WHY this works is because the "cheeks" are pushed apart and you are more "open" to "go" easier.

PS.
I don't know if it's recommended for a child as young as four, but maybe
some kind of fiber mix. (Something that will dissolve completely, I had to
do this once before the "new" fiber drinking mixes that dissolve completely and are virtually tasteless. You can put it in plain water or any kind of juice. (I don't think kool-aid would be a problem, either.) Good luck!