I've been there. It happens. Sometimes you reneg on an offer from an employer. Sometimes an employer rescinds an offer they've made to you. It's something to avoid if possible, but it happens. (Also: Congratulations to you on getting not just one but two internship offers!)
There's no good way to reneg on a commitment, so if you're going to do it, do it with as much professionalism as possible: tell them quickly, with clear and decisive language, while acknowledging and apologizing for the effect it will have on them. If there is something you can do to help them mitigate the negative effects, offer that. Either way, prepare for some blowback.
What I don't know about your situation is whether or not this is something that's going to negatively affect the company you're renegging on. If not, then probably it's as simple as just emailing them to tell them. However, if the company is going to be negatively affected (like if they need to go out and spend more time doing intern recruiting), then you're probably going to need to acknowledge that right up front and it might be wise to prepare for some pushback. If they express that they will have to go back to do more recruiting, you may want to decide whether or not you are comfortable spreading the word about the opportunity with your network of peers. That's up to you.
Watch out for them trying to pressure you to take the internship anyway. If they do that, please make sure you're doing what you believe is best for your future.
The thing that might go wrong here is that your reputation could be negatively affected. You don't want people to say "Don't give her an offer. She might decline it." Before you've even started your career, that's pretty unlikely. The worst case scenario is probably that they reach out to your school to complain. It's possible. But unlikely. I'm not saying this to scare you, but rather just to plant the seed of what the possible downsides are, so you can recognize it if it comes.
Either way, I'd say that this is definitely to be avoided in the future. If it happens once, that's fine. But if it becomes something you do more than once or twice over the arc of your career, it could have reputational impact for you if the industry you're entering into is small and well networked.
Last comment on this one: it's really important that you make the absolute most of the internship you WILL be doing this summer. The best way to make this uncomfortable situation disappear is to do a fantastic job of performing extremely well in your summer internship. Go above and beyond. Double and triple check your work. Communicate openly and often with your supervisor. Etc. Good luck with your internship!
Here's an example note for you to consider (you should edit this heavily to match your situation and your voice):
I have had a major change in plans for this summer and I will no longer be able to join you as an intern. <<<Insert an explanation here if you feel comfortable doing so>>> I'm telling you as soon as I learned of the change, and I'm very sorry for the inconvenience that this change may cause. I am at the start of my career, and still learning much, but I do understand that this is not an ideal situation. I hope that we can remain in touch and possibly work together in the future if opportunity arises. If you need to attract other intern candidates, I'd be happy to pass out a link to any future job posts or internship posts you might have to my peers if you would like that. If you would like to discuss further by phone, please let me know. Sorry again for the change of plans.
Source: I also once renegged on an offer that I'd previously accepted. It had a negative effect on that company, and to this day it still bugs me. Also, now I'm an employer, so I have that perspective as well.
Jared recommends the following next steps:
- Read 3 questions on CareerVillage about how to do well in an internship
- Show up on day 1 of your internship with a one-page worksheet titled "what a wildly successful performance for me as an intern looks like" and ask them to sit with you to fill it out together