Sorry to hear that. I hope they pull through. Just a tip about the packaging: I know UPS actually trains their employees not to read anything on the packaging except for the actual UPS shipping label, so writing things like "Fragile" or "This side up" is useless. The package gets handled by many people while its in transit, so if its packed in a way that it can possibly get broken by anything other than extreme abuse, then the shipper is taking a gamble. UPS doesn't have any special fragile package handling service, so its best to assume its going to get beat up and plan accordingly. I would assume FedEx operates in a similar way.
If the package still has to stand with a particular direction upward, the best thing to do is to put the shipping label on the top side of the box. When they go down the conveyor belts, boxes are always placed label side up, because the scanning machines are above the conveyor. The package might still get laid sideways on the truck or wherever else, but at least when its getting sorted at a facility it will be right side up.