And even after Ivy realizes that she's better off accepting the help than not, she can't manage to maintain her grip. As she falls, you can actually hear the concern in Carmen's voice as she calls out to Ivy.
At the beginning, when Carmen infiltrates the ACME headquarters and meets back up with the Chief, he gleefully thought she was coming back for good. It's pretty telling that, even after all she had done in the past, he seemed willing and eager to welcome her back.
Carmen: Don't you ever try anything like that again!
After Carmen steals the orphanage she once called home, Zack and Ivy decide to leave her be, as it was the only home that Carmen had ever known, and it was scheduled for demolition the next day, anyway.
"Follow My Footprints":
When it looks like Carmen has died, Ivy, Zack, and especially the Chief are devastated. The Chief even becomes sentimental and tells Zack and Ivy how much they mean to him. At the end, Zack and Ivy even go to the Himalayas where Carmen's plane crashed to leave a rose. Carmen herself is happy both that Zack and Ivy are indeed her worthy successors/advisories and that Zack, Ivy and The Chief care about her.
The whole reason Carmen had Manny "kidnap" the Chief? To play chess like they did every Christmas when she was an ACME agent. Not to mention her growing concern for the Chief suffering a viral malfunction and not wanting to lose him; if nothing, it cements Carmen as a Thief with a Heart of Gold who still cares for her former partner.
After Carmen eludes every ACME Detective at once, the detectives find that she left them all Christmas gifts. Each turns out to be a doll that teases that it is the only Carmen that they would ever catch, and wishes a Merry Christmas. Cue Ivy looking wistfully over her shoulder and whispering, "Merry Christmas, Carmen."
When Zach and Ivy find Carmen's Halloween party near the climax, they see Sara Bellum handing out candy to trick-or-treaters, undoubtedly on Carmen's orders. Carmen, being an orphan, wasn't going to wreck the holiday for little kids.
While playing The Matchmaker was mostly to aid Carmen in distracting the detectives from her true objective, after Ivy and Josha have a date together, Carmen tells the player that she did enjoy playing Cupid.