What approach to take?

Firstly, 'phone your son. You have to know what IT is. How can you possibly make amends with your daughter-in-law, if you don't know how you've offended her?
If possible, cut down your visit to two (at most, three) days, and just see how you get on. (Four days is a long time, if things are awkward.)

I think IT is a red herring! When DS said “might make it worse”, my reading of that is that it would make the ‘situation ‘ worse, not alluding to any particular problem. If DIL doesn’t get on with her own mother either, then it’s a problem she has with relationships not an unknown incident that has coloured everything else. DIL is just a difficult person. Go along to see them, stay in their home as invited and enjoy the company of GCs. Ignore old frosty knickers!

Go!
The positives outweigh the negatives: you get to see and spend time with the grandchildren and your son; you can admire the extension; you may discover the reason for and deal with IT, and you don't have to organise Christmas.
You appear to be the adults in this scenario, so follow the wise advice for a charm offensive, respond to every negative with a positive, and have suggestions for other activities to leaven the atmosphere, if there is one: treats such as the pantomime, cinema, restaurant, shopping, long walks etc. Four days isn't that long, with children to engage with.
It would seem that as your daughter in law has a difficult relationship with her own mother, the problem stems from her; she may be one who is happy to accept a gift (for extensions) but resents the giver, as seems to be increasingly the expectation on here. I don't blame you for not wanting to pay for accommodation when you have helped provide extra for your family.
As you live in different countries I am assuming that the 'not talking' is via technological communication, phone, emails, skype etc, and she hasn't actually physically refused to speak when you are face to face. Even if she does, there are plenty of other people about to talk through, and you can just put it down to sheer bad manners.

Easybee I think the comment about not paying for accommodation when you have helped provide extra for the family is possibly the attitude which could have caused the problem in the first place. It infers that the money was conditional and you think they now can expect certain rights because of it. I gave my dd and sil some money to help with her house, however I would NEVER expect any rights over their house because of it. A gift should be unconditional, if not don’t give it, or it can cause major issues if it is “cast up.”

I gave each of my 3 children a fairly large sum early this year......one of them doesn't even want to know me now.....even though I am hurt, I will never throw it back in their face......it was a gift and that's it, as far as I am concerned .

I read the comment the same way as vickymeldrew. Just that you might make the situation or the relationship worse not that there is some particular dragon to be slain. He was just trying to keep things calm and I can't see why he is being criticised. It is his mother and his wife and he doesn't want unnecessary conflict.

My main concern here would be that, since I don't know what I 'did/said' to cause such offence then I might just go and repeat the disaster in innocence.