I totally agree Flipchart that human emotions can be quite complicated and that you can't apply a one size fits all rule to these situations. It's great, obviously, and no-one could dispute that, that the people you describe have all found a way of getting on with others in circumstances many people might consider a bit unusual. Presumably, that's been possible because the personalities involved connect with each other in a positive way and everyone concerned 'gets' something out of the relationship. An individual should, IMO, be free to pursue whatever relationship/friendship they wish .......
....... but, and it's a big but. When an individual's desire to have a relationship with whoever has repercussions for someone else, then it's very selfish to steam ahead with that without first having discussed the situation with the person who'll also be affected by your decision - or, to have 'discussed' it, but still do exactly what you want regardless even though someone else you'll be affecting has reservations and concerns.
And that is where the OP finds herself. This isn't really so much a debate about the merits - or not - of 'unusual' relationships and situations, what it is now is all about one half of a couple totally ignoring their partner's feelings and making unilateral decisions even though their other half will also be affected. He's being really arrogant - why do his wishes trump hers ? Why is she apparently allowed no say regarding guests in her own home ? Why is she allowed no say about additional expenditure which might (as we don't know their financial set up) have a knock on impact on her standard of living ? That might sound 'mean' because I'm aware a small child - who is in no way at fault - is at the heart of this, but nonetheless they're all valid considerations ........ and where does it stop ? He's basically saying it's his way or no way, with no attempt to compromise if this is something he feels strongly about. In the OP's shoes I'd like to hear from him just why he thinks this is such a good idea - I'd want to pin down his motives .... because if it's simply about appeasing his ex (why ??) I'd not be happy. If he was coming at it from a genuinely altruistic stance, as in believing this child was genuinely upset and hating the thought of it, I might be more prepared to seek out a compromise (such as the occasional day out up there) ...... but one which was far less 'full on' than an extended weekend (4 days) and one which had to be approached very carefully so this child's future expectations were managed realistically and kindly.
Quite apart from the fact the DP doesn't appear to have thought this particular occasion through properly (the 'arrangements' re: homesickness seem rather flaky for example) I do wonder what will happen going forward ? What if it 'goes well' and the child's eager to do it again ? Is it fair to say no to him after his hopes have been raised ? ....... will the DP be agreeing to further visits after this irrespective of ex's claim it'll only be 'this once' ? Still seem very very odd that she should say that - if she was genuinely concerned that her youngest was somehow losing out when his sister visited her dad, she'd surely be angling for more frequent visits (albeit that I personally think that's odd) ...... if he's that upset then surely a one-off visit isn't going to cut it and resolve this ? So why the insistence on THIS time, why couldn't a longer visit take place at a.n.other time after there'd been a few day trips ? I smell a rat as many others have too - I bet she's going away.
Having said all that - regardless of what the ex is or isn't doing, the core issue remains that the OP's DP has disregarded her feelings and made a decision without any concession towards her concerns. This doesn't bode well for the future and must be very hurtful for her to realise he holds her in such low regard.