Wal-mart is or is not the very worst place to work. I have several other large corporate candidates in mind that may be quite competitive, based on what I've seen in my life. What Wal-mart does have is a very practical and large scale approach to HR. It's all about them, and it's all about the profits. You are basically a nameless, faceless unit, and they'll follow the policies they've got in place to the detriment of the individual at the corporate level every time. The local managers do have some small amount of leeway that they can give to people, mostly those who have not come under the gaze of policy makers and enforcers of policy. And those local managers are encouraged and rewarded for following the company line right down the line and being totally merciless too. It's all about those profits, folks.
What I find disturbing about this person is the typical addictive behavior mindset that the world has to give me the breaks. It's not FAIR if they don't. THey can't do that to me can they? And when yes, the world answers yet again that it CAN be unfair to you, then that's a ready made excuse to give up my sobriety and start using again, because after all, it's just not FAIR, what they did to me.
OP, as far as what you can do, with all seriousness, I would suggest you go to work as long as they'll let you, do your best, and be ready to accept that you may be sent home. You may, seriously, try prayer, but otherwise, there's no control and no response for you at your level if they decide they have to let you go because of your charges except to gather yourself up and try to find another place to work. Those people who you've worked with there may be helpful to you if you've impressed them with your good work and good attitude, and eventually you'll find a niche. But don't expect large employers to make exceptions to their standard way of operating for you just because you're so exceptional.