Part of the Reason Tisna hates Tarro Blood so much is that him and his lackey came very close to killing Acasha. The lackey even pointed his blaster at her after killing the others. However, even as scummy and dishonorable as he is, he couldn’t bring himself to shoot a sleeping baby. But just the threat was enough to set Tisna off and make her determined to destroy both of them.
Mandalore the Vindicated adored Acasha the moment they met. Tisna picked her up after her adoption when she went to an uninhabited planet with Mandalore for a few days so he could teach her the basics of being Mandalorian, so of course, she took her daughter with her. After all, Acasha is mando now too, even if just a mando baby and it’s not a particularly dangerous hunt, so there’s no reason that Acasha can’t go with her mother and grandfather while they hunt and camp for a couple days. It’s good for her and Tisna doesn’t have to carry her much anyways since the moment they meet, Mandalore carries his new granddaughter as much as he can, or the baby will let him. Mandalorians may have a strong parent/grandparent instinct, but babies are still babies around people they don’t recognize.