bad mother, simple as. if the story is as told of course. noone should leave a toddler alone in hospital. Sometimes it is necessary, if you have other children and no support network to help. But mostly it is not necessary. A call to the school, to a friend, grandparents if you have them near, partner even if separated.
From my 6 or 7 months of DS being in hospital over the past 2 years, we spent 8 hours a day with him when on NICU or SCBU (not allowed to sleep there), and one of us was there 24/7 when on paediatric and he was old enough to notice if we were there or not. only left for a wee, sorted out food in relays, slept alternate nights at the hospital.
Much much harder for single parents, or for those with older children, but not impossible. If you do have to leave you discuss it with the nurses first and explain when you expect to be back. You try to arrange for someone the child knows to come sit with them in the mean time.
I've only seen 2 children left by their parents for a substantial time. One was a 10 year old boy whose extended family left him for about 5 or 6 hours whilst they went home to gather stuff. He was a frequent visitor, knew the staff, understood his dad was coming back, and seemed bored but OK with the situation. The other one was a newborn baby in NICU who never had any visitors. Think the mother must have been in prison or rehab (quite likely), or perhaps a single mum who died in premature labour (very unlikely). The baby did not return to the birth family on discharge. The nurses were extra specially kind to him whilst he was there, and I would have brought him home with me if I could, poor sod didn't deserve that start in life.
Children's needs always come before parents needs. Sick child trumps healthy child but all children need looking after. Its hard to be a single parent but its also very rare for a single parent to have no plan B or friends you can call in an emergency.
I have my judgey pants on tonight, obviously.