I think Ivy sounds better with Kailey, than Reagan does. I also think of Ronald Reagan when I see 'Reagan'. Most people will probably pronounce it that way, so you might need to change the spelling if you want it pronounced with an 'ee' sound.

I think Skye would be a nice middle name. Kailey Summer and Ivy Skye - how sweet.
Also, the name 'Elvy' is sweet and is similar to Ivy.