The way the guinea pig is being held is obviously (at least to someone who knows guinea pigs) way too rough. Pigs are actually very delicate little creatures and holding one that way really might be harmful. I obviously can't say for sure, but it looks like it's putting pressure on the spine - which can be a serious problem.
The best way to hold a pig - just for future reference - is to scoop one hand under their belly and put the other hand on their back, so they're secure and you minimize their ability to wriggle (they are usually trying to get away when someone is holding them, being prey animals). The sometimes flailing movements they make when being held can cause them to injure themselves, and like I said, they're very delicate and their spines aren't meant to bend like a rat's or other small animal's might. It's also important that they feel safe and secure (such as by being held next to a person's chest). Like I said, they're prey animals and anything you can do to help them feel safe is going to make handling them much less stressful for them and overall much easier for you guys.
I really don't mean to be a "know-it-all" or anything like that, and I hope this message isn't perceived that way - I just thought it might help for the staff and volunteers of your shelter to know how better to handle the little ones.