That would be RBF (replace by fee), where you get to double spend an unconfirmed transaction by beefing up the fee on the later instance. CPFP (child pays for parent) is when you spend the change of your stuck transaction with a massive fee to pull the parent tx in. For the miner to get the juicy fee on the second tx, they have to mine the first one too.
As long as you get a confirmation, you're good.
That explorer is shit, don't use it.
If you have moved all of your coins from the origin wallet to the target wallet as you describe, then you have effectively double spent the stuck unconfirmed transaction you pushed originally. That tx will never confirm now, as it is invalid.