I did some testing and I think there is nothing wrong with the blockchain or coin. The block explorer, statistics wallet, swap wallet, coinsmarkets and my local computer are all on the same chain. All are independend wallets. My PC wallet synced up perfectly from scratch. Current height is 70127, 280 masternodes online and 2595 MH/s mining power on this chain. Looks pretty healthy to me.
The new ZeroSolaris (zerocoin implementation) release will also contain new checkpoints. That will help the network.
If CoinExchange and Coinsmarkets are on different chains then surely I shouldn't be able to send coins to both of them from the same wallet as my wallet would have to be on one chain?.
Both are on the right chain. I just tested CoinExchange. CoinsMarkets should enable Solaris again because there is nothing wrong.
You don't need to do anything. Web wallet is on the right chain.