I'm confused a bit by the bolded part above did you import or export?

According to your explanation above when you're importing the private key that you export from your old wallet to Electrum(new) it shows a different Bitcoin address(Address_1). What you want to get is the (Address_2) am I right?

It seems that you export the wrong private key.

One private key doesn't have 2 p2pkh addresses. It must be one private key for one p2pkh address unless if you are importing a different script type with a different address like p2wpkh-p2sh: 3NhNe... and p2wpkh: bc1q3... as Segwit address.

Can you tell us if what old wallet app you're talking about? Is it the Electrum app or a different app?