Cards aren't generally meant for sending cash -- I honestly don't even know what you mean by sending a remittance using a credit card, or even a debit card. If you're talking about using e.g. Venmo or Zelle, they're generally intended for social transactions of tens/hundreds of dollars, not for thousands, and
especially not for thousands cross-border.
For transferring thousands of dollars, that's what wire transfers are for, and basically every bank has supported them for decades. You shouldn't need any luck at all.