What is this "over" in "reached over to"? direction change or something? Normally "reach out" seems to be used.
ex)After being born several weeks early, the twins were put in separate incubators to give their bodies time to grow and strengthen....Remembering an unusual treatment used commonly in Europe, she broke hospital policy by putting Brielle in the same incubator as her sister. Kryie immediately reached over to hug her sister...
If you reach out, you could be extending your arm in any direction including out in front of you. If you reach over for something, espeically in this context where I think the two babies were probably lying side by side, one child would have put her arm out sideways to the other. Her arm reached over an area of the incubator. It reached across the incubator to hug her sister.