You might be able to use https://opentimestamps.org/ to provide evidence over time (i.e. proving it wasn't fabricated all at once).

Still, that doesn't prove that the individual points weren't fabricated at the time.

Another question is if this will be admissible in the court.

There isn't a blanket reason why it wouldn't be. In a particular case it's up to the judge, and the judge's decision probably depends on the quality of the experts that can be found to explain it.

I am not a lawyer but it would seem if you attest to the fact that it is reliable data it would be admissible. Lying under oath and fabricating evidence is still against the law.

> To disprove her allegations I wasn't involved in the kids school and activities...

There don't seem to be any criminal charges here.

That doesn't mean you don't get sworn.

Blockchain?

"I was on Mars on 13/10/2017"

Still a lie, even in the blockchain

The SMS part would mean you could in theory subpoena the telco for proof of that part if it came down to it.

They accept paper logs as well. Infact many judges just order paper logs

It was enough for the GAL to make a positive recommendation, and that seemed to be what the Court was after (the recommendation).