What is the meaning behind this scene in American Sniper where the nurses ignore Bradley Cooper and his crying baby?

One of the key focuses of the movie was to show how PTSD affects families. This scene and others are in the movie to show an indication that Chris Kyle is suffering from PTSD.

Here is a snippet from a Psychology Today on this topic.

American Sniper - The portrayal of PTSD in this academy-award winning film

Chris/Bradley starts to show many of these symptoms, mostly in-between his second and fourth tours. He remains adaptively sharp and competent on the battlefield but during his brief re-integrations into normal society and home life there are some telltale signs: we see him uncomfortable in his own skin, anxious about being away from the battlefield, lost in thought (awful war-related recollections) and, less frequently, sucked back into some re-experiences. He is also adamantly opposed to his wife’s efforts to discuss his experiences and, in general, seems unable to relax into his old life and affable persona. His default mode at home is irritable and guarded; he is visibly edgy when lawnmowers sound off, and inappropriately panicked when his infant cries.

From the medical side: The nurses were engaged with other patients (infants). The nurse rocking the baby was tending to that infant, while the other nurses were doing like-wise. They are professionals and no one likes to be told how to do their job by a layman.

Also, we are not aware of the interactions with his baby by the nurses previously to when the scene begins-someone may have just been with his baby and was now tending to others. He was distressed by feeling out control at what he perceived was the baby's distress without knowing what attention she had received previous to his arrival at the window.

He started off polite but his anger escalated inappropriately-- because of his PTSD.

Also from the Chris's perspective, one of the issues that was at the core of his PTSD was his survivor guilt, or the desire to save more of his comrades-in-arms. This sentiment, coupled with the natural new-parent hypersensitivity, hit two triggers at once when he saw his baby in a situation of distress where he was unable to render assistance.

Babies cry. A baby crying for a little bit is not that big a deal, though it will distress parents, especially new ones. It's pretty clear that the point of the scene, and his freak-out reaction to the situation, was to illustrate the impact that war had on him, in the form of PTSD, despite his outward appearance/facade of being calm, in control and unflappable.