Your being welcome depends on the practice. Some are enthusiastically welcoming and some not at all. We have discovered that attitudes can change rapidly if the two of you make an exit if there is an issue. It is your prerogative if you want to make a stink on social medial etc about them not being SO friendly, though it may save some other couple the hassle of dealing with them. The sole choice, IMHO should be with your SO.
As far as where you sit and what you do. I tend to sit when the dr comes in, and if something interesting is going on AND the SO does not want me in other places, I am pretty good at quietly getting up and observing from a good vantage point, but also a safe distance, The care provider does have a job to do and you should not be i theri way. I don't ask about looking, but I am careful to let them do their job, and truthfully, most of the time they are concentrating on doing their job to the point that they don't even register me.
At the same time, I am there to hold my SO's hand or what ever should she want my attention.
It is an interesting experience. For me I am torn a lot of different ways. Obviously it is hot all hell seeing your SO being probed in the stirrups. No getting around that. And if you go to a ob/gyn you know everybody there is in for a probing, so even just the vibe in the waiting room is a bit hot. watching the girls get called back, and watching them walk out, imagining the goo seeping out of their orifices... At the same time, I am very technical so I can also be very into watching how they work, how they do things, and ponder why they do things they way they do. I bite my lip not to ask questions unless invited to do so, or afterwords to clarify something. And there is my SO's state. If she is in pain or just suddenly wants support, to be there for her. There are a lot of things going on all at once in my head. Your experience may be similar. We always are like supercharges animals when we get home though. (smile).
We have had one provider and she has often commented on how I accompany the SO and take an interest, she has told me she wished more men took an interest. I found that interesting. She has occasionally noticed me watching and explained things to me. Quickly and very professionally, but certainly in a welcoming fashion. We have actually pondered what she thinks of us, but all of our contact has been totally professional, but it goes to show that some providers actually welcome a positive male presence.
I hope all goes well for you and your SO and you have an agreeable practitioner. If not, you can always shop around.