Raya's impure regression would be her crying and being hesitant to call Naamari 'ma' because she misses her birth mother, her saying sorry for how much she gets injured and how much trouble she can get into.
Naamari's impure regression would be absolutely breaking, it's the only time she ever let's herself cry, and she has to be very upset to even do that. She apologizes for her tantrums, and for what she did to Raya. She even claims she 'killed' Sisu when she broke the dragon gem. She's been through so much.
Some of the first times they both regress are impure and it breaks the others heart.
After a bit impure regressions only come after a really bad day or because of some trigger but you described them perfectly