My dh was hounding me for months to get a check up and I didn't want to, either. I finally made an appt and had to take my kids, who are 4 & 8. I left my 8yo in the waiting room alone and he was fine. I don't see any reason why you can't or don't want to leave a 7 & 11 yo in the waiting room.
By the way - I am sooo glad I finally made that appt. While the dr didn't find anything serious, we did determine I needed medication and I am starting to feel like my old self again and not feeling bad and tired all the time.
I think you will be glad you went. I wish I had gone last fall.