How can I do this "account swap" without losing stuff? Both accounts are mine, technically....

You'd either have to keep using both accounts or just stop using one of them. Anything you purchased on the throw-away account would be repurchased on the one you want to use and you'd have to start any progress on games over on those.

I need to delete an xbox account with my email on it, so I can change the email on the xbox account I actually use to the email on the account I deleted.

The account I actually play on and want to keep: Dawglover222

Account that needs to be deleted: PlumDay44983524

Someone set up my account with their email, and for something I had to make my own xbox account with my own email, so how can I use my email on the first account?

I don't want to delete the gmail email itself on the account that will be deleted, so what should I do?

Both accounts are technically mine, and the person who set it up for me does not use Xbox services. Their email is only going to no longer be affiliated with the first account, the one I wish to keep.

What do I do?

Per https://support.microsoft.com/en-us/account-billing/how-to-close-your-microsoft-account-c1b2d13f-4de6-6e1b-4a31-d9d668849979

"You can't use your old account name to create a new account after the account-deletion wait period expires."

As far as i am aware (someone can correct me if I am wrong) once you delete the account you wouldn't be able to use the same email again to create a new account.

Also the xbox account and email are essentially one and the same so since the first account was created with someone elses email the xbox account technically belongs to them. At least thats how support would typically see it.

Basically, you can't. The Xbox account and email (Microsoft account) are the same thing. There's no way to delete an Xbox account without closing the Microsoft account. There's no way to merge accounts and nothing can be transferred between accounts.

The throw-away account has a few Destiny profiles I haven't used in two years and one free game I regret downloading. I don;t care if I lose the throwaway.

I'm fine with deleting the account I don't use, because I don't use it. I just wanted to know if it just deletes the email itself or not. Both accounts use Gmail, but I can delete the account I don't use so I can change the email on the one I do use.