Is it ok/recommended to tell the doctor that you're getting 2nd opinion from that you're coming to them for a 2nd opinion?
Yes because everyone will want to share records / data. The specialized clinics / centers are used to this role! Especially if you are going from a more-generic to a more-specialized center, but even if you're walking down the street.
This is literally life-and-death. My recommendation is for full transparency, it was crucial for us.
Default to telling everything to your physicians. A good physician will have zero qualms with you getting a second opinion.
To the doctor you're getting the second opinion from, don't tell them the first opinion right off the bat until you've heard the second opinion. This to not put them in a position where they feel any pressure whatsoever to agree or disagree to the first. You want their own uninfluenced opinion. Afterwards, yes, you can tell them the first opinion, so they can give their separate opinion on that.