Ok. I can only give you a man's perspective on this. Also this is about Sex so we need to be grown up, open and honest.
...is it ok to control when someone else has sex...no. So you can't do that.
It seems the issue is not first or second but the fact that second for you is second best, and simply not as good.
However from your language you sometimes don't say sex, or love or intercourse but use the phrases like "does me first" or he "does" her. And when your "done" first its "faster" and "harder" and he's "all over you". So I could guess perhaps your a bit submissive, and you perhaps want the man to "take" you and give you good, hard, passionate sex? And second sex doesn't fit the bill. Well as I said you cannot demand he doesn't have sex the same day but I think your completely ok to set out clearly your sexual needs for satisfaction and also try and accommodate his.
Personally I probably have sex or masturbate daily, but even being fit and healthy with more than 1 orgasm a day I know subsequent sex will be a less urgent, less passionate probably less energetic, orgasm will be more difficult and I will ejaculate less. So I would for instance refrain from masturbation if I knew there was a possible sex session on the horizon. Or try not to have two sessions with different partners on the same day, or try not to orgasm with the first. Some men "recover" faster than others for me in reality I can do it several times a day if the mood is right, but to be fully recovered to perform 100% takes me a day. Two days is even better. So anyone who had second sex on the day with me would also be getting second best. So I understand your issue. But I don't find second or third or whatever sex gross.
I'll be honest and say my "recovery" is not always what my wife sometimes needed and some days she sometimes needed more "satisfaction" than I can deliver and hence how our relationship has developed to what it is now. I don't see anything wrong with that.
So I do think you need to tactfully talk to your boyfriend about the performance you need so he can consider his own behaviour and performance and perhaps help him manage that. But tactfully it's a sensitive issue.
I have a long term very long distance girlfriend who I see when I can and she made it clear to to me a long time ago that when she sees me she expects in her own words: "a good seeing to" or a weekend "sex fest". I see nothing wrong with her setting out her needs and desires and me trying to comply with them. That may take some abstinence from masturbation, some partner planning, but aslo some joint work in our case it includes uniforms, sex toys, text sex, talking dirty, and role play to make sure it happens. You may want to consider some of these to help him help you.
I assume despite you mentioning they wanted a unicorn that a threesome for first sex is not an option?
I'm also going to mention Viagra. Legally prescribed by my doctor (don't get ripped off on line) who knows our relationship and lifestyle, it certainly helps me on the occasion when a bit of "help" is needed to avoid disappointment