Declining an already accepted offer.

[writingmachine]

I applied to 3 different programs this application season (a post-bacc and two master's programs) and heard back from both the post-bacc and my second choice master's program at a state university (actually my alma mater). My first choice program runs on a later schedule than the typical deadlines, but I hadn't heard anything from them so I wrote it off as an implied rejection and went with my second choice which I was perfectly fine with accepting. Then to my surprise my first choice program contacted me at the end of May and invited me to interview two weeks ago. They offered me a spot this past Wednesday and I couldn't turn it down.

First choice: Nationally ranked. Has offered me a fully funded master's, stipend, and benefits which I sorely needed (was just kicked off my family's dental insurance after turning 26 last month).

Second choice: My alma mater. Decent school with good reputation in the area, but an unfunded offer with no stipend, and no benefits. I was fully prepared to foot the bill by working full-time even though it would be tough. 

Now I realize I'm faced with an ethical dilemma and I completely understand the potential consequences of declining an already accepted offer. I'm not sure if asking for release applies to me in this circumstance. The only paperwork I signed for my second choice was a half-page pdf where you either checked off that you accepted the offer of admission or were declining and if applicable where you would attend instead. My app fee was waved due to being an alum and I don't owe, according to my student portal, a deposit of any kind. I was to be billed in August and was going to set up a payment plan for the year. On Monday I plan to e-mail the grad admissions office and be upfront and honest. Then I plan to e-mail my adviser and be upfront as well and thank them for their time.  How exactly should I word an e-mail of this nature to both parties?