How you approach this will depend on what tooling you have
available.
If you have a stretcher/shrinker, see where on the ring the tapered
holes touch. See if you can grab just the outer gold rib, depends on
how ‘domey’ the ring is. If it contacts the insert first you might
get away with merely shrinking it since you’re only going a half
size(but can you be sure the insert is solid? If its hollow in any
way you have a problem) If it does touch just the rib, shrink the
gold portion until the platinum insert gets loose. If you’re lucky
you will be able to shrink it enough to just slip the insert off. If
you can only go so much before contacting the insert then maybe you
can slip a sawblade under the insert and saw from inside the insert.
Once you have them separated you need to calculate the required
inside diameter of the insert. Shrink the insert just a skosh
smaller, like a quarter size or so… Then shrink the gold ring
smaller til the insert can be just worked over the rib with some
effort. Now stretch the assembly to size, clinching the insert in
place.
If you need to cut the insert, the rib is in the way, isn’t it?
Rather than saw right thru the gold, saw just enough to cut thru the
insert and peel it off. Use plat hard to solder the insert back
together at the size determined above and gold solder the cuts in the
ribs. Shrink the ring as before, reassemble and stretch. The reason
not to cut right thru the ring is that a butt seam won’t be as
agreeable to stretching. Naturally its preferable not to have to fill
with solder but sometimes you can only do what you can do.
If you don’t have a stretcher/shrinker you’ll have to cut right thru
the ring, do similar to above and stretch it on a smooth polished
ring mandrel. Depending how heavy the ring is you may have to sweat
some.
That’s if you really need to retain the original look of the ring.
If you have some latitude and the customer doesn’t object to a
deviation(the seam between rib and insert will be filled with solder,
you can neaten this up to an acceptable level with a sawblade and
polishing brush) at a lower cost you could simple solder the insert
to the ring before sizing in the usual fashion. Use 20K white welding
on the platinum, 18YH on the gold and rhodium when you’re done. Not
purist but gets it done easier and cheaper.
This I know from experience will work IF the materials are suitable
to the process.