Have MIL put a white noise machine right next to your daughter while she naps to drown out the dog. Our daughter always naps longer at home than at school. We just put her to bed earlier on weeknights to make up for it. Also, at that age, our daughter was falling asleep on the walk home from school after work. Things like strollers and car rides put kids to sleep easily, and at that age they are still napping multiple times a day. I wouldn't be too concerned.
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