Bitcoin Private Key Question If Bitcoin can be forked, and the same address can exist on both blockchains, what stops the re-generation of a privatekey on one blockchain that would also work on the other? 

For that matter, what stops someone from forking the technology, starting from the genesis block, and using a program to endlessly create addresses > Search those addresses on the Bitcoin blockchain > if the address on the Bitcoin blockchain contains funds > use the newly generated privatekey to access the funds on the bitcoin blockchain?
A Bitcoin address is computed as follows, according to the Bitcoin wiki: 


A private key is a 256-bit integer $k$ below 0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141, the order of the group $E(\mathbb F_p)$ of $\mathbb F_p$-rational points on the curve secp256k1, $E/\mathbb F_p: y^2 = x^3 + 7$ where $p$ is the prime $2^{256} - 2^{32} - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1$.
A public key is the standard encoding $\underline P$ of a point $P = [k]B$ on secp256k1, the scalar multiplication by $k$ of the standard base point $B \in E(\mathbb F_p)$.
An address is the ‘base58’ encoding of the string $\text{‘1’} \mathbin\Vert h \mathbin\Vert c$, where $h = \operatorname{RIPEMD160}(\operatorname{SHA256}(\underline P))$ and $c$ is the first four bytes of $\operatorname{SHA256}(\operatorname{SHA256}(\text{‘1’} \mathbin\Vert h))$.


If you could find $\underline P$ given $h$, you would be given top billing in a top-tier cryptology journal.  This is because it would tear down the widely held conjecture that both RIPEMD160 and SHA256 are preimage-resistant.

If you could find $k$ given $P$, you would also be given top billing in a top-tier cryptology journal.  This is because it would tear down the widely held conjecture that discrete logarithms are hard to compute in well-understood elliptic curves like secp256k1.

You would alternatively be able to make money from exploitation of much more lucrative markets than your own private blockchain or cryptology journals.  But there are lots of very very smart people in cryptology who aren't doing that, and it's not just because they're all paragons of morality.