I didn't see anything about courts, but no matter.
"Connie" has at least four options, and they're not mutually exclusive.
1. Work out a written agreement on her own with "Brutus." This should cover decisions re the kids (braces? summer camp? haircuts?), visitation (when? who will pay? etc) and child support. From what you've said about "Brutus" this is unlikely.
2. Move with the kids to Ohio. (Legal as long as the father knows where she moves to and how to contact his children). File with the state child support agency for child support.
3. Move with the kids to Ohio, and file a petition in court for custody, visitation, and child support.
4. File a petition in CT for custody, permission to move to Ohio, visitation, etc. Wait to get a court order prior to moving.
The only legal way for Brutus to try to stop the kids from moving to Ohio is by filing his own court action, or winning the case that Connie files. There is no legal way for Brutus to stop Connie from moving.
I'll assume that I have answered your question and will "ACCEPT" my answer unless I hear back from you with follow-up questions.
Bonuses of even a few dollars are much appreciated.
I REALLY appreciate POSITIVE FEEDBACK!
Jane Doe Deer