Usually the guidelines aren’t absolutely specific (from my memory). For example, child X doesn’t have to have 3 vaccines on birthday Y. A month or so was not only allowed at my practice (and the one previously) but completely understood by the pediatrician. Personally, if a doctor’s office threatened to call CPS for a 30 day delay before another vaccine, I would look for another doctor. They would be the same practice that called if the child was 5 pounds overweight or other such nonsense. I think the biggest factor is the time it takes for a parent to reschedule and keep the appointment. I realize a lot of Moms work and taking off may be an issue. However, I’d do it again in a heartbeat and have recommended it to many of my younger friends just having babies (all of whom have taken my advice)
You don’t have a choice to look for another doctor. This has happened to someone I know personally. You either get all the vaccines they think necessary, right then, or they call CPS and put you under investigation.
I personally asked why my child needed the Hep B vaccine immediately after birth and was told it was necessary and any refusal would necessitate a call to CPS. This was at a major hospital in the biggest city in the state.