I'm a little confused, because in the Op you state the mother isn't lazy, but wants to 'baby' her daughter, yet later on you state she is lazy. It can't be both?
Ultimately, (and I am both a step parent and parent myself) it is none of your business if your SD lives with her Mother. Parenting is best between the parents and your husband seems to disagree with you here an dthinks his daughter should be wearing the pull ups at night. I fhe agreed with you, then that is a different situation, but as long as there is no welfare issue, you cannot control what happens when your step daughter is at home with her own Mother. Exczema is NOT cause dby bad hygene though, it is a skin problem. In fact, excessive bathing/showering worsens it.
It may well be that your SD is suffering from nocturnal enuresis. Suprisingly coomon and something like 1 in 11 9 year olds have it and still wet at night. It is also recognised that children can subconsciously controlt heir wetting n certain situations, so if your SD is aware that you disagree witht he pull ups it may be the case that she is able to be dry at night when with you, but not when at home with her Mother.
My stepson has nocturnal enuresis and whilst I don't really agree with the pull ups approach, it's not really my place to judge others who do use this method, especially if it causes less stress for the child. Perhaps the best course of action is to ask your husband to speak to his ex about seeing a doctor if his daughter hasn't already, although usually the medical profession will not do anything until the child is about 7.