If the former First Ladies usually go, then I think she should.
The fact DT didn’t go to Biden’s would just show she is being the bigger person.
If they don’t normally go, then probably not, up to her.
Having said that, I remember seeing at Trump’s inauguration, he and Melania arrived at the White House to be greeted by the Obamas. Melania presented Michelle with a gift, as is apparently traditional, Michelle more or less tossed it aside with hardly a look.
Whatever their feelings about the new Presidency, I thought that was extremely ungracious in front of the world’s cameras.