My mum was recently a pathology collector for about 18 months. Anywhere is happy to do 2 kids, but only if there are 2 collectors on hand.
Mum didn't do any kids. She didn't feel experienced enough to get in & out quickly without traumatising anyone. I've only had it done with mine (DD2 mainly) a few times, but DD2 has a 'nice thick layer of fat' (paeds words) & has been pretty much impossible to get blood from. Every time taking up to an hour... the only time they actually got a vein, she was 8 weeks old. It wasn't pretty

Make sure you book in advance (some places are take a number) & I think kids do need to be explained to a little... depending on age. I know DS handled his 4yo vax so well coz he knew what was happening IYGWIM...