If your going to be in the bathroom for more then 2-3 mins then you absolutely should put her I. A chair and strap her in or bring her with you .... What if she climbed up on something and fell off or jumped off and landed on another child or what if she purposely hurt another child? There are all kinds of scenarios that could happen while you are in the bathroom for an extended period of time .... You should be protecting the other children and yourself from accidents as you are liable if she hurts her self or another child while in your care.
As for potty training I always use plastic pants over thick underwear to protect my furninshings and at this age .... Yes I absolutely agree with a punishment for soiling themselves .... At his age she knows the difference and she is making a choice not to use the potty... Is it available to her to just use all on her own or does she have to ask you? I have two potties right outside my bathroom and I have three kids that use the potties ( two I put on and one goes on her own) and I have one that uses the toilet. If you don't have something that she can just use independently then maybe that's what you/she needs ..... However I think this family needs their walking papers and I would not ask them to pay for the doll .... If it was not a daycare toy then it should not be out during day care hours... But I might be inclined to mention it to the parents. Good luck