This is Shayn from Crossref's support team. I can only officially speak to preprint repositories that register DOIs through Crossref (e.g. bioRxiv, chemRxiv, Research Square, SSRN, etc.). If they're registered through DataCite (arXiv, Zenodo, etc.) or another DOI Registration Agency, there may be different practices or guidance.
Crossref's perspective is that, whenever a work is changed in a way that would impact interpretation or credit, the new, updated version should get a new DOI. It essentially becomes a new and distinct thing. That new DOI should then be related to the original item's DOI in their metadata records. (the preprint repository should be able to handle that)
So, in this case, each of your two new preprints should get a new and distinct DOI. The original DOI should not be re-used. The original DOI should continue to refer to that original preprint, which is a distinct (though related) work from either of the new ones. But, they should be connected in their metadata using an inter-work isVersionOf relationship. DataCite has a similar relationship for versioning in their metadata schema as well.
The citations will be split amongst them, but in this case it's appropriate that they're split. Your original preprint and your new preprints are not the same work, so citations against them should be distinct. Someone citing one of them is not actually citing the others.