Hello Peachey, and welcome to Offshore Outlaws!
I have a Predator 165 and I'm inclined to agree with you - it can fish two brilliantly, but three would be a squeeze.
As for the rest of your requirements - you'll likely need to make some compromises/trade offs. For example, a boat that can fish 3 in comfort will be larger, therefore heavier, therefore less suitable for trailing and slower, unless you go for a bigger engine, which means more initial outlay, bigger fuel bills etc etc.
How often would all three of you be fishing? If it's only occasionally, you might find a 165-style boat would fit the bill more often than not. Give us an idea of frequency and estimated budget and we can better advise. Off the top of my head I'd say a Raider would suit you, but these are heavier to move around on a trailer. One of the guys at my boat club recently sold his Raider as it was too heavy for him to manoeuvre single-handedly when getting it to the slipway from his yard space.
Whereabouts are you launching from? I'm at ECA in Langstone Harbour and can give you some pointers on beach launching if necessary.