Hmm... you say you used a vinyl tablecloth protector, huh? 
That would certainly explain why you found it very difficult to tear it. Should be fairly easy to cut through, so long as you have a decently-sharp pair of scissors or some other sufficient cutting tool to work with.
As interesting and unique an alternate material as that is to use for something like this, I honestly don't know if it'll really be good for sanding or detailing.
I mean, given the thickness of it, to try and sand it so you can get a smooth enough paint finish on it, you could very well end up sanding through it in spots. That obviously wouldn't allow for an even finish.
Not only that, but I would imagine when sanding it, depending on the sandpaper you use you could end up with some really deep scratches.
You would then have to sand it further to get the smooth surface you want, which could result in the possible sanding issue I mentioned in the second-last paragraph.
Also, in regards to the application of this material over the Pep model, you'd have to stretch it a bit and maintain that rigidity so that it would form over the base model properly.
You'd need to use a stronger adhesive as well. A glue stick (even the industrial-strength kind) or contact cement most likely wouldn't do the trick.
Then again, based on my experience on working with different plastics for various scratch-build projects, that's just my take on it. There's no reason why you can't give it a shot and see how well it works for you...

That would certainly explain why you found it very difficult to tear it. Should be fairly easy to cut through, so long as you have a decently-sharp pair of scissors or some other sufficient cutting tool to work with.
As interesting and unique an alternate material as that is to use for something like this, I honestly don't know if it'll really be good for sanding or detailing.
I mean, given the thickness of it, to try and sand it so you can get a smooth enough paint finish on it, you could very well end up sanding through it in spots. That obviously wouldn't allow for an even finish.
Not only that, but I would imagine when sanding it, depending on the sandpaper you use you could end up with some really deep scratches.
You would then have to sand it further to get the smooth surface you want, which could result in the possible sanding issue I mentioned in the second-last paragraph.
Also, in regards to the application of this material over the Pep model, you'd have to stretch it a bit and maintain that rigidity so that it would form over the base model properly.
You'd need to use a stronger adhesive as well. A glue stick (even the industrial-strength kind) or contact cement most likely wouldn't do the trick.
Then again, based on my experience on working with different plastics for various scratch-build projects, that's just my take on it. There's no reason why you can't give it a shot and see how well it works for you...