The short answer is "no". The CF can barely cope with intact families, let alone ex-boy/girlfriends. The system will only engage and even consider altering its plan if there is a roadblock.
Is there a custody agreement? If no, there is nothing the CF can refer to in considering this case. If yes, who has primary custody, and does the agreement restrict where the primary custodian may relocate? If the mother is primary and the agreement does not restrict her geographically, then once again the CF has nothing to refer to. If the agreement does restrict her as to where she may live, she has a legal problem to consider as the CF will still likely post the member regardless. From the CF's perspective, a CF member married to a person who is legally unable to leave e.g. BC is useless to the CF as members must be mobile. The system will make this a personal problem and post the member regardless, and start an admin review if he objects to the posting.
Whether the mother/step father want the move to happen or not is irrelevant as the CF will post them regardless, so do not let this be an avenue of hope. The stepfather could try to seek social worker intervention to stop the posting and keep the larger family intact, but I doubt this will be effective as I am not reading anything about special needs, medical issues, etc, in your post. The sad truth is we have separated and blended CF families everywhere and the system does not cater to this. The system does not even keep intact families together with every posting.
I apologize if I am coming across as being harsh as it is not my intent. You have simply asked a loving question with the best intentions to an organization that sees people as capabilities vice individuals. I have seen this 101 times and it always goes in the favour of what the CF wants and needs. The old adage remains very true still today - if the CF wanted you to have a family they would have issued you one. Have a look at what I wrote above and see if there are any avenues for you.