recycle pet bottles using some injection molding?

It is possible, but the remelted plastic isn't as good as the virgin plastic.

There are lighter solvents and hydrocarbons that are mixed in the virgin plastic and when you reheat them the solvents evaporate a little and the plastic isn't as flexible or strong. It is still very useable (you have to keep the different types of plastics separated...PET, LDPE, HDPE...styrene...etc)

If you look at any consumer plastic bottle out there, you usually see something like 30% recycled plastic used in manufacture. This is because of the difficulty of getting the same plastic from recycle suppliers to the manufacturer, since the scrap dealer usually grinds up the plastic and a few other plastic bottles get in the mix and a plastic like PET doesn't take kindly to other plastic types.

In fact, PET bottles rarely use any recycle plastic in their manufacture because of this. Plus like I said, the plastic loses some of it's lighter components in reheating.

Sort of like trying to make a cooked cheese sandwich and reheating it a few times...it just starts losing moisture and flavor.

But if you have pure PET bottles and just want to use it in small batches, you can reheat it and inject it into molds. It just won't have the strength and impact resistance that virgin PET has