(Cheerfully with great enthusiasm) "Honey, I know you like company at the doctor, so I'll be there. Don't worry, you're NOT bothering me. I'm glad to do it."
Just go with her. Don't do it in a spirit of being needy (how would YOU showing up at HER doc's appt be evidence of YOU being needy?) or smothering. Do it in a spirit of "that's what loving partners do for each other."
YOU: "I won't hear another word about it. I'll be very glad to go with you and be supportive."
HER: "I'd rather go on my own."
YOU: (very cheerful) "That will work out even better for me. I'll meet you there." (Then you call the doc's office tomorrow to make sure of the time.) "And I'll take you out for lunch afterward."