The normal procedure when requesting cancellation is for them to terminate the service at the end of your current month, with the reason being that you've already paid for it (if on automatic billing). However, as far as I know, immediate cancellation should be an option, which means terminating your service today instead of at the end of your current month and crediting the rest of the month's fees, which you would ultimately get back. Why they refused this option I don't know. I also don't know why they said next month if this was the last day of your current month.
As for the equipment return kit, you should receive it within a working week of the date of service termination. HughesNet needs to receive the equipment within 45 days of service termination so as to not be charged for it. For reference, this is the procedure for returning the equipment. It's a PDF.
I'm sure a rep will either confirm or correct any of this information.
Thank you for posting again. @GabeU is correct in regard to the normal procedures for canceling an account. Your service was successfully terminated and you should not be charged for the grace period. This grace period is available just in case you are unable to find another provider in time or simply change your mind. What I will do is monitor your account to make sure there are no charges for the grace period. If there is one, for some reason, I will waive it immediately. Alternatively, you can call back in and request a termination revision in which it can be re-processed as immediate. I would do this for you here, however, I am unable to initiate or alter terminations through our social media platform. This is due to account security. I am also unsure why this was not done in the first place, as the case notes do not indicate the reasoning behind it. I apologize in advance for any inconvenience this may cause.