Aye mama I'm with the others here, seems a bit uneasy. I personally enjoy 1st date sex or whatever. I really don't want to "rain on your parade" if you're excited about this guy. But the whole "meeting at home" thing is a red flag for me.
(I'm not ashamed of anything, but when I started dating, I did accept a couple of "meet me at home for a movie" first meets and although nothing non-consensual happened, things happened that I wasn't happy with afterwards, with guys I wouldn't have been interested in if we'd met in an outside environment. Just because we "started off in the home location")
1 You shouldn't be worrying about him "thinking you don't trust him". Even when I've had casual lovers before, the etiquette is they ALWAYS offer "out" option or "home option". Eg my ex and I met, and we were getting quite drunk and flirty, then he said "coffee at my hotel room OR would you rather stay out and go somewhere else".
If they guy is pushing for the "home option", it means he's trying to override your instincts, which is a bad sign.
And if he's saying "do you trust me?" he's being a fuckwit. It's not actually ordinary to say that? Decent men don't say that, they recognise that women have a need for safety and work that into their planning. Eg I've been chatting with a guy on POF, and he's suggested going for a day trip with him driving, but then also said "we should meet for a coffee first in the City Centre, so you know I'm ok". That's pretty "standard" behaviour. Anything else is abnormal.
2 Practically. I'm a bit confused. Can you not just either not drink or have one at the start of the evening, then not drink for the rest of the evening? Therefore transport option sorted. Or meet for a coffee? You don't need a mega long first date, if there's a connection you can fit in a second one sometime.
Either way, I'd text him to SAY you're not staying over (not in an angry or questioning way, just in a "oh realised I've got an early start on X day, shall we just meet for a couple of soft drinks or a coffee?").
I think you'll get information from how he answers that. There's nothing wrong with a man wanting sex (and of course you might want sex too if you fancy him, nothing wrong with that) but manipulating a situation so that he can override your instincts is a very bad sign (to me)
Good luck Sorry if it anything in this post came across bossy or nagging btw!