You will still get the first original full refund (and keep it) or pay the first tax due. You should not amend or change your return until you get the refund from the original return or your payment has cleared.
The amended return will only show the difference you get back or need to pay. You can confirm this by printing your amendment and looking at the 1040X. Line 18 should be your original refund amount and line 21 should be your additional refund. If you paid on your original return it will be on line 16. If there is an amount owed with the amendment, it will be on line 20.
If you owe on the Amended return you have to include a check. But why do you say the correct amount should have been larger? Then you say send cash with the 1040X? Are you expecting more refund or to pay some of the original refund back? Usually adding more income reduces your refund.
The 1040X form for 2018 hasn't been approved yet by IRS. Please, keep checking the following information on how to amend your return; it will be updated once the 2018 form is released:
https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed
