Here is something to question them about. Breastmilk has more calories than formula. All breastmilk, yours too. So what would adding formula to the equation accomplish? If anything they should recommend more breastmilk or an evaluation of how much mik babe is taking in (perhaps a tongue tie or other issue is preventing babe from taking in a good amount). However, with adequate wets and poos, which you have, it indicates your babe is absolutely taking in enough. Therefor if babe is still not growing in a way they feel is healthy they need a gastro work-up or other medical testing. Formula has no place in the equation. In terms of hospital I'd call and simply say you are not ignoring their advice, you are taking them seriously, and you have decided to get a second opinion. Even if they did call social services as long as you've booked a second opinion they'll see you are taking it serious. I'd get recommendations of breastfeeding friendly doctors before making that second appointment though.