I think shadowing is an excellent idea and I wish it was a required part of recruitment on my unit. I don't know how many new hires we've lost over the last few years because they discovered that working on our unit was not what they thought it would be. Our hospital has basically wasted tens of thousands of dollars to poor screening and poor orientation. Having said that, my intention isn't to discourage you but to give you a little insight. Working with critically ill children and their families is hard work... physically, psychologically and spiritually. It can also be stultifyingly boring one minute and terrifyingly chaotic the next. An example of what I mean could be coming on shift in the morning to an assignment where you have a stable, ready-for-the-ward patient who has been held in PICU due to a lack of ward beds and could maybe even go home. You barely get your safety checks done when a code is called on one of the peds wards and the code team rushes off to the rescue. Now you're reporting off to someone else on the patient you haven't even introduced yourself to and setting up for admission of the child in distress upstairs. Depending on what caused the arrest, you could be racing to stabilize the kid enough to send them to the OR for emergent surgery or continuing with resuscitative measures while an ECMO circuit is primed and the child is cannulated.
A lot of people think that PICU nurses spend their days cuddling babies, playing video games with older kids and checking the occasional vital sign. Not so much. Shadowing will show you only a smidgen of what our shifts are actually like, but it would still be very valuable. Shadowing is just that. Observing. You may be offered the opportunity to help with turns and diaper changes but will do virtually no hands-on. The point would be to gain some vicarious experience and insight. It's a chance to see it all first hand and to ask questions. Ask lots of questions - about staffing levels, education, staff development, morale, interdisciplinary relations, available resources and anything else that occurs to you as the time passes. But most of all, be honest with yourself and with the unit; if you have any misgivings about working there, be they personal, professional or institutional, don't take the internship.