breastfeeding support

My son just turned 1 month old. Breast feeding has been going great for us. He had no trouble latching and the lactstion specialist at the hospital was very happy with how he was feeding. At his last appointment he had gained almost a whole pound in a week and the pediatrition was really happy and said 'keep doing what your doing mom'. He eats like crazy and has plenty of wet/dirty diapers. Well every time we have a tough day because of not sleeping well or crying more than normal my SO always says 'want me to go get formula?' Or 'I think he would stay fuller longer with formula, people keep telling me that'. Well his mom had also mentioned that I should get formula for when I go back to work rather than work on building a supply in my last few weeks off. Then I come to find out that she's telling him that he needs formula to sleep better. It's so weird to me because his sister is the biggest breastfeeding advocate that there is and feed her baby till he was over two while also feeding a newborn. His mom is super close to her and very supportive of all her parenting choices so I'm just confused as to why she's trying to get me to use formula when she knows I really want to breastfeed and to me it's going fine. I'm feeling super unsupported now and doubting myself, wondering if I should start supplementing with formula.