With families of multiple marriages, it would be great it would be great if you could simply select the child with the mouse and move it to another parents pair.
I believe FamilySearch purposely makes some things "more difficult" in order to encourage users to carefully review the matter before, say, taking a one-click or drag-and-drop action.
In the case of a child that has been added to the wrong set of parents (in some cases it is just the mother that is wrong) I don't find it too much bother to copy the child's ID, then add it under the correct parents, then immediately click on the pencil icon (by the child's name against the wrong parents) and Remove the relationship with these wrong parents. (I usually add a reason statement of "Now positioned under correct set of parents.)
Fortunately, FamilySearch are no longer making some actions as easy as they were in the past (e.g. the merging process), by now providing warning notices and encouraging us to provide reason statements. Making an action quicker or "more straightforward" is not necessarily going to lead to us making correct decisions - very possibly the opposite.
Actually, I just realised there is an easier way of correcting just the one parent. Again click on the pencil icon, but (on the Parent-Child Relationship page) click on Remove or Replace under "Mother". Check the "I have reviewed..." box, then "Replace Mother". On the Replace Mother page simply enter the ID of the mother you wish the child to be attached to, and follow instructions from there.
Yes, either method is a bit long-winded, but at least it provides time to think about ones action, rather than simply dragging with the mouse, without any need to add any reason for the change.
Additionally - in the case of multiple marriages - the child may have had Step, Adopted, or some relationship type (other than Biological) - the child could also be listed under the other 'parent' with that relationship type (so the child - with same ID - could be listed under both sets of parents).
It does complicate the Tree when the child could be listed under multiple parents. I guess Set Preferred Spouse (which is slightly different in New Person Pages) - is the best way to handle this situation for Pedigree/Tree viewing ease.
Drag-and-drop would be a Bad Idea in the Family Members section: it would make it way too easy to unintentionally rearrange a family.
It's not a single step, but it is possible -- and actually pretty simple, once you grasp the structure of it -- to move a child from one set of parents to another. You do it by editing the child's parental relationship(s). Paul described two of the ways to do this: you can add the child to the correct parents, then remove the relationships to the incorrect parents; or you can replace the incorrect parent with the correct one.
The remove/replace function is actually pretty forgiving: in most cases, you can achieve what you need by approaching from either direction. I personally find it easiest to always start with the child, because you're less likely to end up with an unintended single-parent relationship if you're dealing with both parents at once, but I can see how "one at a time" could be simpler in many situations.