Yeah, but spidey works and is going back to work, and her child has been in daycare in the past and will need to be there in the future since both parents work.
From what I have read, it is best to get children on the long-term routine they will be in before a major change like a new baby, and to maintain that routine no matter what, which is what spidey is doing by sending her daughter to day care. Many experts think it is good for children to have their own life and peer group so they do not completely rely on their parents for validation and attention.
I think it sounds like typical 3-year-old behaviour as well (no 3-year-olds myself but I know and have known plenty!) My mama said we all went through mama stages and dada stages. The changes of pregnancy and a new baby may have increased it a bit. I would do what you can to show Q she is loved - try to have a bedtime routine with her (bath, story etc.) - get hubby to watch the baby for that half hour or whatever. Find something for her to do with you while you nurse the baby - Mama used to read to one child and nurse another at the same time, or let the other children snuggle beside her while she nursed, or we would all sleep/rest together. You can get her involved with you and the baby by "letting" her help you with little things and make little decisions (like what the baby should wear.)
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