somewhat lost

I have been doing my type of work (very well to be honest) for almost 20 years now. This past March I was laid off (been there 2 years) and received a small severance. This October, my immediate boss called me and wanted to hire me back! Very happy with the news, had to go in and meet with his boss to make sure everything was under the bridge, which was and got hire papers to take to HR. Had to redo all paperwork and all that was left was my drug test. I go to the clinic while drinking plenty of tea (I'm somewhat a camel). I'm led to a tiny bathroom with some guy following me. I find out its a supervised urine test. All a sudden I can't go. They tell me I have 3 hours to takes the test and am given a glass of water. Then another, and then they bring me half a glass saying that's all they could give me. With the 3 hours almost up, I finally have to go. No being 6' and 400 lbs, it is not easy for me to reach my penis to urinate. I did not know it was going to be physically impossible to do that with one hand and hold a small cup with the other. It was quite humiliating, my legs shaking, sweat dripping everywhere while trying to preform this physically impossible act all the while having a guy watch me and trying to give advice on to reach this way, stretch that way, I had to steady myself with one hand on the wall just to keep my wobbly legs from collapsing. Making matters worse, I lost the urge to urinate, not that I could without another hand. It was a horrible and I was nearly in tears. They let me call HR, so I could ask if I could to a hair, blood, or even a saliva test, at my expense, explaining that I physically could not hold my genitalia and a cup at the same time and urinate, thus again reliving the entire ordeal at the nurse's station and the rest of the world. After speaking the 2 HR people in charge, they both said no and resended my job offer. On properity, if there is an accident, we did a mouth swab. What, if any, recorses do I have available? Can I be denied employment, from a place that employed me, for a job I am able to do and do well, because what I stated above. I am still willing to pay for my own drug test. Thanks to anyone one who can help me.