Like all things in life, you get what you pay for. The court has no authority to stop the utility companies from coming after you, all the court can do is enforce her end of the bargain.
Talk to legal aid for assistance. This is a post-decree matter, but since this appears to be a contempt issue, you will want to check the county local rules (I don't know if you're in Cook, DuPage, Kane, etc) for how they handle "Rule to Show Cause" petitions - especially on how they want your ex notified.
Again, self-surgery is cheap, but if I want an Appendix removed properly, I pay a surgeon who knows what they're doing.
Unfortunately, given the facts as you describe them, it is highly unlikely you will be able to find an attorney to take your case on a pro bono basis. All that attorneys have to offer is their skills, training and experience. You are asking an attorney to do a great deal of work for no compensation.
This is not a case that would qualify for pro bono legal work from a licensed attorney. You might contact the local law schools (there are many) and see if any have a legal clinic. That said, since your name was never removed from the utilities or mortgage, you're always going to be responsible. If you had a lawyer the last time around, it looks like there are loose ends.
I agree that this does not sound like a pro bono case. Without knowing more facts, Judges generally enforce court orders (like your divorce Judgment) based on what is written in the agreement. If it says she needs to indemnify you for utilities, then the court the court would likely make her pay. You haven't stated what her argument for no paying would be. Having a father who is a high profile attorney probably won't help her. Did her father represent her in the divorce?
For informational purposes only. Not legal advice.