As someone who has suffered from insomnia, I know how devastating it can be to have nightly disturbances. It could become a medical problem for your neighbour very quickly - many people can't get back to sleep again after being woken once, or develop migraine/sleep disturbance problems, or depression if they end up a significant amount of sleep on a regular basis - or they simply may be too incapacitated to do their job effectively, which could impact many other innocent, vulnerable lives, depending on what she does. It is not as simple as 'I have to feed my baby and everyone should work around me'.
I do understand what it's like to be obsessed with your first-born and everything relating to them, but there's no reason why anyone else should be. You can understand that your DP needs to wear earplugs (which is why he sleeps through everything, BTW!) because he has to get up to do his job. It's exactly the same for your neighbours; they have to sleep. She isn't even asking you to move the baby (though I would move a baby in a heartbeat to improve a neighbour's chance of a good night's sleep), she's simply asking you to move yourself. When the books tell you to sleep in the same room as your baby, they don't mean every second of the night. You don't stay beside your baby for every second of their day time naps, do you? And it's not as if your baby will even be alone for that time. And obviously you can take a monitor if you need to hear them....it sounds like you just don't want to get out of bed really.
Medical kit is oxygen tanks, hoists, incubators, that kind of thing. And even then it would be nice to work around others in every way you could - I say that as someone who knows disability from the inside. I can't begin to understand how you could, as someone who is personally experiencing how horrible sleep deprivation is, know there is someone getting tireder and tireder in the next room, without the massive accompanying joy of a new baby in their lives, and not give a toss, even though it's within your power to fix it. I don't get how anyone can be that selfish.
Try removing DH's earplugs and see what it's like to share the insomnia around a bit - perhaps it will help you to understand why this is an issue for her. After all, it's not fair that he's getting a good night's sleep while his baby disturbs someone else's sleep.