I think you shouldn't rely too much on saying you can't go due to pressures of work, commitment to other things, etc, as it allows them to persist in the belief that if they keep moving the parameters you will eventually have to cave and say yes. And it keeps the door open for them to contiune with the unacceptable behaviour. It needs to be brought to a head.
So, this is what I think should happen now:
If the holiday is mentioned at the funeral your DH should say very firmly and without hesitation:
Yes, I do need to talk to you about that, but now is not the time. Let's discuss it later.' And then refuse to engage over it any further, so no scene will be caused at the funeral.
MIL and/or SIL will be bound to phone him at the first opportunity after that. If TV answers the phone and they ask about the holiday she should say 'Oh yes, DH wanted to talk about that with you, hang on...' and she should not engage with them over it.
Your DH should keep his voice quiet, calm and measured, speak slowly, and he should say (making it quite clear that it is HIS decision)
' TV and I have had a long talk about this Mum, and we are both in agreement that we think it would be a very bad idea to go away on holiday with you so we will not be coming. I am sorry, but we will not be changing our minds.'
She will ask why, and he can say:
'Mother, I have something very important to say and I'd appreciate it if you would really listen, without interruption, and take it on board.'
'You and DSis are obviously very close. DSis has made it clear many times that she is not terribly fond of TV and frankly, you seem to collude in her nastiness, and you seem to enjoy ganging up on her in what you think is a very subtle, passive-aggressive way. Maybe you don't even realise you are doing it, but I DO notice, and it upsets me.'
'She may not be your favourite person but she IS mine, and it hurts me to see you and Dsis constantly trying to point-score over her, and make her feel like an outsider. I know we can all get along just fine in small doses, but I will not put her in a position where she is made to feel uncomfortable for a whole week. I've seen her bite her tongue many times over the years, in the face of huge provocation, for the sake of harmony in my family. She does not deserve it, and I will not watch her have to do it any more.'
'So, in conclusion, thank you for the kind offer, but we will not be coming on holiday with you. We will go out for a birthday dinner or do something nice together for one day, when you get back. But you need to know that in future, if I feel that either of you are being anything other than pleasant and civil towards her then we will leave immediately. We will not shout and scream and fall out with you over it, or start hurling accusations - we will just make our excuses and keep cuting our visits short until you get the point. If the two of you cannot manage a whole visit without a sly dig here or there then you will be seeing a great deal less of ALL of us, because we only come as a package.'
'I am going to go now, and give you a chance to process all this. I am not going to have a row with you about this, but I realise you will want to respond, and I will listen, providing you are calm. But not right now - perhaps tomorrow, when you've had time to think about what I have said. Goodbye'
Yes, I know it sounds like a mammoth prepared speech, and it IS. I think it's important that it comes across as such, because then she will know he really means business, and it isn't just some half-hearted spur of the moment whinge.