Are you from the UK? By law you are allowed to take any time you need to visit any antenatal appointments, this even includes NCT or pregnancy yoga, but of course it's best to put these outside work so not to piss of your employer And yes in this law they allowed to ask for your proof of your appointments. Though at their discretion but they are completely allowed to do so. It could just be upper management of a procedure they need to follow at your work place Honestly though I know how it feels, feels like your not trusted and your making it up :(
My job does this but I know my job isn’t all jobs so I don’t know if it relates but it’s pretty common for if we have to be out to provide a doctors note. It’s not to point us out for how much we have been out it’s to show each of our times missed were for legit reasons when our reviews come around because they are considered “excused absences” rather than just calling out and doctors/ dentist/ etc don’t “count against us”
I did this a few times during pregnancy (including when my provider recommended I work from home) and no I don’t think the employer is asking for any super personal information (or if they are they will not receive it anyway). Basically you just need your provider to say you need imaging or something along those lines. Tell them it is for work and they will know how to deal with it. In my experience they never disclose protected information about your health or procedures.
I think it's okay, I think they're just doing their due diligence