(I might interject briefly that you are not so fat that your hand gets stuck, but you probably are wearing a wrist brace from last night's set of pushups which were painful, and not in a "Work it, G.I. Jane" sort of way. It was more "Your wrist might possibly snap in two if you continue" sort of way. So you made yourself do seventeen, primarily because it's what a Navy Seal would have done, minus 200.)
So, hand stuck firmly in the mail chute. You might panic at this point. After all, here you are trapped in a federal post office mail chute, all suspicious like, one arm reaching inside for far passed any polite time frame. There are no cars behind you yet, but anyone could see you and call the cops because tampering with the mail is a federal offense, dude. To any passersby you could be stealing rent checks, or disposing of your unfinished slurpee, or unleashing a cat or ANTHRAX - WHO COULD FORGET ANTHRAX?!?! In fact, Jack Bauer is probably already onto you. (But only seasons 1-5ish Jack Bauer, because we can all agree that seasons 6+ were a complete.waste.of.time.)
You have to escape. You can't go to prison. You have a husband. You have children. You don't even *like* bologna. (In fact, you take a second in Mommy Judgement and SuperiorityVille to congratulate yourself that your children don't eat bologna. This congrats will be diverted by the memory of a recent lunch where your children dined exclusively on m&m's and cheese nips.) Children need their mothers. And not in prison.
You come up with a plan reminiscent of James Franco in 127 Hours (because you are that committed to staying out of prison), minus the drinking your own pee part (because you are not that committed to staying out of prison). But the blood would surely lead to you, especially because you have a pretty rare blood type and DNA testing is kind of specific. The next obvious part of the plan is to employ vampires to clean up the blood but remember they don't exist (except for Edward and the rest of the Cullens - don't spoil it for the kids, kay?) So, in a moment of brilliance you think, "LEECHES! Leeches TOTALLY exist!"
You are trapped inside this minivan and mail chute. Thankfully, you have four children with you, three of whom routinely find disgusting nature like stuff outside and bring it two inches from your nose for you to examine. There is a pond a half mile away. You could send them to gather some leeches ...
...but then they would be ACCESSORIES and they would go to jail.
At this point you will tug really hard in desperation, and your hand will come free.
This entire thought sequence will take place in approximately SEVEN SECONDS. So, go you for your quick and logical problem solving ability.