Frustrating appointment

I mean I’m happy it went well, but here’s the back story. When I found out I was pregnant for peace of mind I booked a private ultrasound at 6 weeks. I went to that and was told I was measuring behind and to come back in a week and baby would be there, so I did and hallelujah baby and heart beat we’re there 😍. So tech said I was measuring for May 30th. Today I went in for my first actual doctor appointment, I had my intake and pregnancy confirmation a few week ago, but got a pelvic exam and was told I’d get an ultrasound for measurements. Well all was good at first, this doctor is temporary until insurance kicks in to find a new one, but I got a pelvic exam and then went to their ultrasound room. Well the ultrasound was super outdate so I was bummed I wouldn’t be able to hear baby’s heartbeat. It was also abdominal which I thought was strange so early because technically based of May 30th I’d be 9 weeks. Well she quickly measured sac and said I was measuring 8w 3D which puts me at June 4th due date but never measured baby or anything else and it was done. I have 2 problems with this due date, one being this puts conception on September 11th but that’s 4 days before AF was due and I got my positive that day so that makes no sense and 2 why didn’t she measure baby? I booked another private ultrasound next weekend because they took measurements of everything and will allow me to listen to heartbeat thankfully. But this has me so confused. I’m grateful I saw baby and heart flicker but sad it wasn’t what I expected