Which summer internship to take?
Since these are both REUs, I do not think attending school 1's summer program will affect your chances of attending grad school and continuing in academia.  Most REUs are designed to give students an opportunity to see if they can conduct scientific research and / or enjoy it.  Depending on the university and the discipline, they may be considered 'recruiting' camps for people to attend that university's grad school program in your discipline.

Since you have a fairly strong inclination to working in academia, you do not need the experience other than to confirm your suspicions and to make you a better candidate when you apply to graduate schools.

As for what I would suggest --- ask when you think the earliest day / time you would be able to get a response from School 2 on acceptance or rejection, and then from there, try to see if you can eke out some more time on School 1's deadline so that you don't end up shooting yourself in the foot.

You may also be able to talk with your current PI and see if he can hear anything through some back channels as to whether or not you have a decent chance.

At the end of the day, it's up to you.  Consider all your options wisely.