Divorced for 42 years...completely estranged but my two daughters in touch with him

[Swizol]

I have two lovely daughters who live close and we have good relationship.
I have been remarried for 39 years but my daughters who are in touch with Ex...250 miles away...!!!. Constantly have to answer X's details about my life.
It sickens me...I have told my kids not to share, but they say he badgers them.
I am so angry about this and I keep telling them not to discuss me

Your daughters should be respecting your privacy and shutting down his attempts to pry. But for your own sake I think you should try to care a bit less about what he knows or thinks he knows. It doesn't matter - he doesn't matter.

Tell them to feed him BS

What is their relationship with him like? They could either make an effort to be non-committal (eg: what's your mum up to? Oh not much, you know, just pootling along) kind of thing. Or just say "I don't know".

But do you think they are telling him because they want to? In which case, I would be wary about telling them too much to be honest.

That would annoy me too. You need a discussion with your daughters where you make it clear they are not to discuss you with him. Emphasise that it upsets you. Make it clear that his badgering the m upsets them, so how do they think you feel? Make it clear that you have no issues with them having a relationship with their dad but your life is not up for grabs.
How does the topic arise? Do they bring it up and complain? If so, it's easy to say the answer lies with them cutting short their visit. If you bring it up, then you are equally as guilty as he is!

It's interesting you phrase it as 'in touch with my ex'. Is he their father? Doesn't mean they should be sharing information about you life but it if he is it isn't surprising they are still in touch no matter where he lives.