A couple of things may help you out:
#1 You can pick up some epoxy putty at Home Depot (the paint dept.) that is designed for use on plastic/fiberglass/PVC. Just clean the area with alcohol, pull off a plug, knead it until it becomes one solid color (off-white), and press it into place. It'll set up in about 10 minutes and cure in a couple of hours. It's waterproof, so it should last forever. If you put it on the underside, you may not even see the repair from the top side (depending on the size of the hole).
#2 If you go for a replacement sink, keep in mind that your RV sink is not the same size as a household kitchen sink. It's a lot smaller. You can probably order a replacement sink the same size from Home Depot in either acrylic, quartz, or stainless steel. Being a "non-standard" size, it will cost quite a bit, though. Finding the same sink at an RV dealer may be less money. If your countertop is laminate (Formica) like mine, you can cut the hole larger with a jigsaw or a Dremmel Tool to accommodate a larger sink. Just make sure it will fit into the cabinet below the sink.
#3 If you repair it, or replace it with a similar product, be very careful of heat. Thermal shock can be as destructive as direct heat. I always recommend running warm water into a cold sink before you dump hot water into it - like when you drain pasta. The warm water will temper the sink so it doesn't crack from the rapid expansion of "thermal shock".
Just my 2 cents!