I can only echo what the vast majority of other posters have said and repeat that he is being utterly and totally selfish, arrogant, thoughtless, bullying etc etc etc.
This has nothing to do - really - with whether or not it is "appropriate" for a child to witness a birth, nor with the fact she is a step child ...... but everything to do with who you want to be with you when you give birth.
If there is one occasion in her life when a woman is allowed to be totally "selfish" with extremely good reason, it's when she's giving birth. YOU get to choose who's there, YOU get to choose who visits and when. If you want your husband with you, you'll want him to be a support to you ...... not an effing childminder, for goodness how long. You want him to be wiping your brow, physically supporting you in a position you feel comfortable in, getting you a drink, reassuring you if/when things get scary/painful, you want him to speak up in support of you if there are decisions to be made and you might be semi-comtose/exhausted ..... and 1001 other possibilities which can happen when you give birth.
No-one can possibly predict and be 100% sure how their birth will go - even mums with lots of kids. I'm not going to list all the ways in which things might go "wrong" - and obviously, I sincerely hope they don't, but there is lots of potential for you needing his attention to be 101% on you.
That's before you start wondering what effect various things might have on the child. TBH, that's the last thing you should be worrying about right now - that'd be his fault if she was traumatised in any way ..... but if it got to a point where she had to be ushered out, then presumably he goes with her, leaving you alone at your most vulnerable.
The more I type, the angrier I'm getting. How dare he expose you to extra worry / feeling self-conscious / feeling inhibited / humiliated / exposed and so on when you will need all your reserves to concentrate on the birth itself. Does the prat not realise that if you feel stressed, it's possible your labour may take even konger ? How dare he demand that you don't swear ........ you should be able to scream and swear all you like and no-one at the hospital will give a toss.
Look ....... have you actually spoken to your midwife and/or the hospital about this yet ? As you could drop any moment, this is imperative. I can't believe for a moment they'd feel happy about this.
I want to come over and slap him for you I really do - knock some sense into his condescending shit for brains. As someone else said, how would he feel about exposing his private parts to a child ..... how would he feel being intimately examined by a doctor while a child watched .... how would he feel pooing himself in the prescence of a child ....... the whole idea is absolutely preposterous and at a time, when he should be putting you first, he is putting what he wants above you. What an utter shit he is.
I am so so sorry you are in this position. You must feel very frightened and bullied.