When Dai is transferred from Ethereum to xDai on the xDai chain, the amount of Dai in your wallet will decrease and the corresponding amount of xDai will increase. However, the transaction will not appear on the xDai side of the wallet. The easiest way to track it is in BlockScout with the Coin Balance History view.
1) Copy the account address used for the transaction.
2) Paste the address into BlockScout at https://blockscout.com/poa/xdai.
3) Select Coin Balance History.
4) Scroll down to see incoming and outgoing amounts. Your transaction should appear here.
Red txs signify outgoing and green are incoming. You can click on the block number to find your transaction in the block if you'd like more information.
5) Select a tx hash to view details.
6) Here you see the recipient address, the value, and the hash of the initiating tx on Ethereum.
7) This tx can be copy/pasted into Etherscan to see the initiating tx information.