Please, please, please beg and plead with your admin to get your floor a vein light. Ask for a private fundraiser, have a bake sale on your floor every week for a year. Do something to raise the funds.
I am a mom who has watched her baby, who is a a super hard stick with crooked veins, be stuck over and over. Now we won't let anyone try unless they use a vein light. We even brought our own for emergency visits to hospitals where our son is not known.
It appalls me that any hospital/lab would not use a vein light on a child. It is one thing for an adult to deal with two to however many attempts, but a child or baby should not have to. They do not have the life skills or even cognition to understand what is happening, much less why they are repeatedly getting hurt over and over. (Yes, this is a huge issue for me after fighting for my son for so many times.)
I have worked in healthcare since I graduated with my Masters, so I am a hospital employee too. It seems it is a patient care issue and nothing else. The vein light allows for access on the first try almost every single time. Why would that not be what should be done every time?
Really and truly, a vein light may not solve the world's problems but it really does help sick babies and kids! (And on a side note warm packs can help too while you are getting the hospital to buy you the vein light!)
Good luck and I hope they come through for you and your patients!
PS: Yes, you need to learn to draw on the peds patients, but as a mom I would have thanked you for NOT trying if you knew you weren't going to be able to get access. So on behalf of that mom, "Thank you."