On holiday and I don’t know if I’m unreasonable!

It's possible Kate thinks she's doing the right thing. Her DH can't do activities because he's working, you can't because of your injury, so it makes some sense for them to do them together.

If that is the case, she's misjudged it (and so has DH by agreeing to it so freely) but the only way to find out and resolve it is to talk to them, maybe over dinner when everyone else is there?

This. OMG what a pair of C☆☆TS im so angry and upset for you OP 😤

your husband getting angry when you brought up about time he is spending with another woman on holiday - as you say is very telling

I think there is something wrong with your marriage and is it worth salvaging or not?

id say to both of them together - im feeling like a gooseberry on my own holiday, not a nice feeling

Careful.a relative of mine went on holiday with his wife and teenage kids, met a family overseas and they all got on well , spent the holiday together , seems the relationship between the wife and the friends hubby started once they got home , they were at it behind his back for a while
Now divorced

Yeah that's not cool - I would be fuming with both of them and would also find it very hard not to be moody.

Kate is being REALLY inconsiderate arranging all these things you can't join. Fair enough they want to do them, but she could at least discuss it with you in a sort of, I know you can't join but I would like to do xyz, we'll be x amount of time and then let's do whatever you want.

Your husband is likely enjoying the attention, when he should be saying no thanks Kate, I would prefer to do something my wife can join in as well.

Who wants to be sat on holiday on their own for most of the day?

Either bring it to their attention how they're making you feel or book the next flight home and leave them to it.

The fact he's got defensive about it says that he knows he's in the wrong. I think your gut is trying to tell you something here. There's obviously an attraction between them, but I'm bloody minded and I wouldn't be dragging him back to my side saying pick me. I'd be on the next flight home.

Why can’t you talk to Kate about it?

I would say “it seems DH has developed a little crush on you. Please don’t encourage him, it’s making me feel quite uncomfortable.”

So would I. Pronto.

I think you need to be quite direct and do it to both of them when you’re all together. Next time they say ‘we’re going running/swimming etc’ can you say something about not wanting to spend the whole holiday on your own?

I think I’d be really pissed off and not sure if this would be the best way to handle it but I also think if anything is building between them they both need to know you are aware and annoyed.

But you can tell her (and your DH) that the way they are behaving is inappropriate and making you feel like the third wheel.

Hopefully she has the grace to be at least a little bit embarrassed. If either of them gets defensive then you might have your answer. They would be realising that they hadn't been as subtle as they thought they had been, and that you were watching now.

They seem to have been pretty careless and blatant to be honest. Your children have probably noticed by now too and it will be embarrassing and hard for them. Do Kate and Neil have any children with them?

I would ask her why she is spending so much time with your husband.

It’s not so much about being assertive enough to state what you want to happen, it’s that your husband and your friend know, or should know, that it just isn’t cool to leave you on your own for long periods of time on what is supposed to be a group holiday. And that you would prefer to not be on your own. Yet they are engineering these situations, because that is what they want. Your husband is spending time with her because he wants to do that rather than include you. She is doing the same.

So you could make your feelings known, and they could behave better, but ultimately they’ve made it clear what their preference is.

Your spidey senses are there for a reason……

I agree OP. Everyone's very focussed on your DH's inconsiderate behaviour (which, of course, it is) but "Kate" seems to be getting a bit of a free pass here. If she's primarily your friend, why isn't she arranging to do some things with you too? I understand that she's potentially at a bit of a loose end with her own DH working, but arranging activities only with your DH is inconsiderate and I'm really surprised she can't see how excluded you would feel. I'd be feeling quite pissed off with her too.

Yeah he’s into Kate and she’s into the attention. I’d be having words with DH.

This. She’s really taking the mick. Pull her up on it. If she feels offended then boo hoo. Why should you be the one feeling irritated and left out.

Then you need to be blunt with Kate.

Actually, sod the beach surveillance.

If your DH genuinely doesn't give a shit that you are upset that he is spending all his time with another woman, then I'd go to Neil and tell him that I am flying home, and why.

Well you can say your DH has other priorities and you’d like him to spend time with you. I’d also be disappointed that my friend invited my family on holiday and then monopolised my DHs time, and that she also didn’t seek me (her actual friend) out. They’re both behaving badly.

Oh and tell Kate your having time alone with your husband and not to arrange any more activities at present as you want to spend time together alone , make it clear to her and stop letting her dictate what is going to happen, be strong woman.

I presume there are deeper issues in your marriage. You say you don't want to risk pushing him away by saying it makes you unhappy ? Why would you fear that ?

If your relationship was working wrll he would be focused on you and enjoying time with you. I would say this isn't really about kate she is a symptom and he is always a shit husband.

What would he do if you arranged something for your family only? Can you try it? If he then says it's unfair to leave her alone - ask him to explain the difference between you and her.

Ask him if he would like you to go home.
Tell him you want to go home anyway - because of his behaviour and you are having a terrible time and he is being ridiculously obtuse if nothing is going on!