If Prince Charles believes his visit to the United States has been a goodwill trip, he's sorely mistaken. His appearance on American soil has caused nothing but hard feelings and bitter recrimination among the mother of eligible daughters in this country.

I was sitting between two of these mothers and the other night at a dinner party and this is exactly what happened.

"I wish Prince Charles would come to Washington," one of the mothers said. "I know he would love to meet Mitzi."

The other mother scoffed.

Why would Prince Charles want to meet Mitzi?"

"Because he's looking for a wife, and Mitzi would be the perfect princess. She has beauty, education and she understands the British pound."

"I never heard of anything so ridiculous. If Prince Charles was really looking for an American wife, he would be much happier with my Caroline. When she was born, the nurse said. 'She's beautifyl enough to be a queen.'"

The first mother said, "Caroline has asthma. She wouldn't be able to live in Buckingham Palaace."

"That's a stupid thing to say. If Caroline married Prince Charles she would install a new furnance with an air-purifying system that would take care of her asthma."

"I'm quite certain that Queen Elizabeth wants Prince Charles to marry somebody whi is completely healthy. After all, the whole purpose of him getting married is to have a male heir. Now Mitzi hasn't even had a cold in her whole life. She is the picture of good health. The Windsors do need new blood."

"In all due respect, I don't think Mitzi is regal enough to be a queen," Caroline's mother said. "It takes tremendous savoir faire to open Parliament."

"Mitzi would not have to open Parliament. Prince Charles, when he became king, would open it. The least you could do is read up on British customs if you want your daughter to marry into the royal family."

The discussion was becoming rather heated, so I tried to add a light note. "Why don't we do it like the TV show, 'The Dating Games.' Prince Charles could sit behind a screen and ask Mitzi and Caroline questions. Then at the end of the show, without seeing them, he could choose over one of them for his bride."

"That would be very undignified," Mitzi's mother said. "For Prince Charles?"

"No," she repied, "For Mitzi. After all, if she's going to be a princess she can't do anything commercial."

"I wouldn't allow Caroline to do it either," her mother said. "I believe Prince Charles should marry for love."

"Do you really think that Prince Charles would fall in love with Caroline?"

"There is no doubt in my mind," Caroline's mother said. "Besides, I know that Prince Philip and Queen Elizabeth would enjoy having us as in-laws. Jim and I are very comfortable with royalty."

"You forgot one thing," Mitzi's mother retorted. "A British queen is expected to ride a horse on her birthday. You told me yourself that Caroline was allergic to horses."

"There is nothing in the Magna Carta that says the queen has to ride a horse," Caroline's mother said angrily.

Finally, Mitzi's mother turned to me. "Let's leave it to Art. Which do you think would make a better match for Prince Charles - my beautiful Mitzi or her asthmatic Caroline?"

I choked on my mousse au chocolate. "What a question!" I said. "All I can say is I don't think Prince Charles is worthy of either of them.

"Now, if you'd like to talk about my daughter, Jennifer . . ."