I don’t think she would have perceived it as playing with them or doing something the family didn’t want.
When she offered a homely service, looking after them as if they were still alive, until it’s time to say your last goodbye, she is thinking about having the tv on, cuddling them etc. Having them in a Moses basket, baby bouncer. There won’t have been any ‘tugging about’, I’m sure she will have cared for them as if they were alive. That’s kind of the point.
Of course some of the parents were imagining what a PP heard from a funeral director- nursery rhymes, nightlights and so on. They were horrified.