Just so you know, I'm writing with the experience of living with at least 9 different muslims over the past 10 years (not including the 4 maids we've had in that time).
Now, to the difference between baths and washing for prayer. Yes they are different, but unless you're physically in the bathroom with them or they leave the door open or paying an obsessive level of attention to them, it can be near impossible to tell the difference. Why? Because the majority of them will use the bak mandi to both bathe and wash for prayer, thus the sound from the bathroom will be the same, only what they wash and how long they take will be different.
As for the other matters, I didn't comment because I agreed with you. However, when I mentioned it to my wife, she reminded me of her friend who had complications and had to bed rest for a week or 2 after the birth, so in that case she did need someone to look after the baby 24 hrs/day. Until you know the circumstances...