“I want my Google Calendar email reminders to a different email account than my Gmail address. There doesn’t seem to be an option in Google Calendar for adding another email address.”
Google Calendar reminders are designed to be sent to the Gmail address associated with the same Google account. Currently Google Calendar doesn’t support adding additional email addresses. There is a workaround to get your calendar reminders to another address, but you need to add a filter to Gmail to make it work.

Gmail allows you to create Filters, which are special rules designed to help you manage your email. These Filters can be used to sort your email, respond automatically, and a number of other functions. In this case, you want to create a filter that forwards email to another email address.
Assuming you want to send every email reminder you receive to another email address, here are the steps to follow. You can create a new filter in one of two ways: a) you can check the box next to one of the Google Calendar reminders in your Gmail inbox and select Filter messages like these from the More Actions dropdown menu. b) Or you can click on Setttings > Filters and create a new filter. Either way the next steps will be basically the same.
To send every calendar reminder to your other email account, you need to add two components to the filter:
1) The email address Google uses to generate the reminder (calendar-notification@google.com)
2) In the subject section you want to include Reminder:
You might be able to skip the second one, because it appears the only mail that comes from that email address is calendar reminders, but I like to be specific in my email filters just in case. After that you click the Next Step button.

Next you choose the email address you want to forward your messages to and create the filter. All future calendar reminders will go both to your Gmail address and to the second address you forward the messages to.