EmilyRosanne
I think you sound like you really believe you're doing the best for your daughter. You sound genuine and although I disagree with some of what you've said, I really hope this has the best possible ending for you and all involved. You're stuck between a rock and a hard place and came here for advice. Of course, some advice will be contrary to other posts.
At the same time, it wrangles me that you think (and to some extent, unfortunately do) have the right to dictate to their father what is best for them, what you will allow etc. You have been taught how to administer the meds but won't allow him to. It sounds like he was busy working while you went to the Dr's. I would feel very differently had he been watching Jeremy Kyle and on the brew.
Because you clearly don't have a problem with his parenting of your eldest, he isn't all bad. His messages sound shitty but not "vile" or "repulsive" as typically hyperbole-loving MN'ers have stated.
I want to address your last post, where you say "But if you put yourselves in the position that it is your child with a life shortening condition where small mistakes could end up really costly".
I realise 'your' could be referring to you and your ex, but it clearly isn't. You view your daughter as more yours than his and this isn't fair. I don't know your daughter's exact conditio and even if I did, I have nothing more that a first aid cert. I have been in a vaguely similar situation to you. Our middle child was born with a life-threatening condition. He took multiple meds throughout the day - some of them critical. After brain surgery at 14 months he is 'fixed'. I was extremely protective of him. Due to DH's work and travel, it was me who spent more time at the Dr, meeting specialists and the like. At no point would I have suggested what DH was allowed to do, what was permissible or that I had any more rights to our son than he did.
Mistakes in you DD's care could be costly. There are possibilities you could make a mistake surely.
I think you're being over-protective and the father is suffering.
I also think he needs to grow a pair and whatever animosity he feels towards you at the moment should be put aside so he can spend time with your daughter and she can be breastfed.
I think her being unsettled away from you is very easily overcome. You need to give him alone time with her and at the moment it doesn't sound like you're willing.