iOS doesn't make this easy without a third-party app like this one:
This is what I do and it works too. No additional apps required.
1. Create a new contact in iCloud (iCloud.com) or from your iPhone or iPad.
2. The company name field is your distribution name.
3. In one email field type in or paste in all the email addresses you want in the format as listed below. That's open double quotes follow by person's name close double quotes. Open greater than sign e-mail close greater then sign. Each additional entry follow by a comma. Last entry you don't need to.
I would suggest do this in Note (on the iPad) or somewhere you can see your entres. Then paste them to the email field.
Good luck! Hope this helps.
Long Beach CA