Is it weird?

My daughter is 18 months and will be 21 months old when her brother is born. I had a bad experience with breastfeeding her(long story short it was so forced on me by the hospital doctors and the pediatrician that it turned me off to it) and she was only breastfed for a week then switched to formula. She had a milk protein allergy and had prescribed formula and even now she has issues with regular milk, almond milk, lactose free milk(it makes her constipated).

Even with my bad experience with my daughter I'm willing to try breastfeeding again with my son(new hospital, pediatrician and city). I wanna ask my pediatrician if I pump for her(after her brother his born) and put the milk in her sippy cup could we see if that helps with her milk issues.

My question for you guys is,is that weird? She hasn't had breast milk since a week old. Has anyone on here done something like that. I won't be putting her to the boob, just pumping.