Does the distinction between left and right hand matter when making an off-hand attack? [duplicate]

Clara the Fighter finds herself facing a huge undead, the Frost Giant Skeleton. She attacks twice with her scimitar, and again with her light hammer! The undead reels back as it takes bludgeoning damage, which it is vulnerable to!
On her next turn, can Clara make the Attack Action using her light hammer instead of her scimitar without switching hands?
Here’s the breakdown (assuming all attacks hit):

Turn 1
Action: Attack (scimitar, right hand) = 2 x (1d6 + Str) slashing
Bonus: Off-hand attack (light hammer, left hand) = 1d4 bludgeoning, x2 because of vunlerability

Turn 2
Action: Attack (light hammer, left hand) = 2 x (1d4 + Str) bludgeoning, x2 because of vulnerability
Bonus: Off-hand attack (scimitar, right hand) = 1d6 slashing

Is the above allowed?