You first need to know what material you're dealing with. You say "plastic" but I'm going to guess fiberglass? If so, as someone else mentioned, be sure the base is supported properly. It's very common in residential construction for fiberglass showers to have a lack of support which leads to cracking. I'm sure an RV is no different.
If you step on the floor of the shower and it moves/flexes you'll need to do something to support it. I've tackled this several times and have used spray foam up under the pan and it works great. Just don't put too much or the super-expanding type or it will break through the pan (this takes a lot so don't worry too much).
Once it's supported to fix the fiberglass correctly is not easy. Fiberglass repair is something I'd leave to a pro. You can put sealers and what not on it but they will not last long. Coincidentally, I just had the fiberglass tub/shower in one of my house's bathrooms redone for $750. They repaired a couple holes/cracks and refinished so it's bright and new looking.
After all this rambling I hope you're actually dealing with fiberglass :) Otherwise, I've just wasted both of our time :) :)