"inconsistent care"

Came three weeks ago with my four year old during a Monday afternoon and staff were incredible. He was triaged immediately then transferred to Lancaster where he was treated for dehydration and tonsillitis. Couldn’t have faulted any of the care we received. However, came back one week ago with my four month old baby who was seen by GP the same day, given antibiotics for a chest infection but who was exhibiting stridor, struggling at times to breathe and had full coverage mottled skin with a fever. We arrived at 10.45 to walk through the door and be stopped before we could even make it to reception by a middle aged lady (at this point I’m holding my 4 month old in my arms, he’s half dressed as he vomited in car, clearly mottled, has loud stridor and is coughing and breathing fast). She informed us that they closed at 11 and stood blocking our way, she must have mentioned several times over and over how they close at 11 whilst in the background two nurses looked on with a look of dread on their faces as if we were going to keep them from going home. I explained the situation to her, that it wasn’t 11 and was told we could use the PHONE OUTSIDE to call 111 or to go to Lancaster. If it’s this important to let me know ten times when you close, you should change the sign to no walk ins past 10.45. We went to Lancaster and called 111 enroute (who urged us to complain given that it wasn’t even 10.50 when we were on the phone to them and their system told them they were OPEN until 11 for walk ins). 111 secured us an appointment with a dr at Kendal hospital (what a completely failed and ironic system) but by this time we were already at Lancaster. My baby was admitted to the children’s ward, treated for sepsis and diagnosed with a chest infection and kept in. It was fairly simple for the receptionist at Lancaster to see my baby needed to be seen urgently but the woman at Kendal couldn’t take her eyes off mine to lecture me on closing hours to even check him. How is it possible that the level of care at the same place can be so incredibly dangerously inconsistent? That a four month old baby cannot be seen before the time of closing? That the sign clearly states 11 closing? I get you want to be home on time, but that doesn’t mean you being home for 11. If they close at 11 but clearly won’t see anyone before a time too close to that to inconvenience them, then they need to change the sign and inform 111. Reading other recent reviews it seems others have had the same problem. I will be putting in a personal complaint and seeking to identify the woman we spoke with as to complain about her personally and the two nurses who did nothing to intervene but looked at us with anxious disappointment.