Tit for tat. If you don’t launch nukes now, they might now think you’ll do it in the future either. Don’t escalate: hit them silo for silo. No major population centers. Strictly military targets, as close as you can manage (obviously some civilians are going to die, but that’s true in any war).
Ultimately, I keep coming back to retaliate in kind, but I would consider a few things.
First, if there are ongoing tensions with Russia that make me believe this might be a tentative first strike, I’ll launch all-out. The OP’s scenario says this is not the case, but no intelligence is 100% certain, especially while the missiles are still airborne. In the presence of an existing crisis, I’d rather just retaliate.
Second, if it looks like the story is true, but we think Russia will have ongoing problems controlling their own people, I may do much more than retaliate in kind, though perhaps stopping short of all-out destruction. For example, if we can isolate Russians rebels to a certain region (Chechnya, say), then let’s go all-out on that region, since the Russians can’t/won’t do it on their own. (To this end, I might launch an immediate retaliation in kind, with a deadline for the Russians to clean house before we step it up another level… but that might be giving them too much room to plan their own all-out attach.)
Third, if there’s any reasonable retaliation in kind that minimizes civilian casualties, I’ll go with that. For example, if we have a carrier nearby and we could accomplish comparable damage to the Russian missile defense, then I might use those resources to limit the number of nukes needed.
Habeed’s point in the first response to the OP is a very good point: From a political standpoint, I have a lot to lose politically if I do not response. From a political standpoint, the Russians have a lot to lose if they publicly admit they can’t control their own nukes. You can’t ignore the importance of either factor - even if politics won’t result in a war right now, you don’t want to set the stage for war next year.