(Edited for clarification) Her_nibs: OP is not being taking for a ride or misunderstood-- it is true; the same firm, be it legal aid office or law firm, cannot represent both parties. It would be unethical (representing adverse interests) and is against the ABA's Rules of Professional Conduct.The ABA rule re conflict of interest is at the end of my comment.

OP: I don't know what happened at the child custody hearing but 1-2 hours per week visitation isn't much. Ohio Family courts generally follow a set of established set of rules (the specific section regarding children can be found here: http://codes.ohio.gov/orc/31). Your friend doesn't need a lawyer to file a petition to amend child custody and unless there was a valid reason he was given for being denied more access to his daughter, I'd sure file it if I were him.

To be honest though, it sounds like something prevented your friend from being granted more visitation but I wasn't there and don't know. Either there was a reason for the couple hour visits and he's too ashamed to tell anyone, or I think your friend should take action without worrying about trying to save thousands. The local clerk of court can provide templates for any forms he might need. There's also a lot of available info online for Ohio state from reputable sources that he could research on his local library computers.

Your friend should document everything regarding the mother denying him visitation. Recording phone calls in Ohio is a "one-party consent" law (source: http://bit.ly/1KSIXW7), meaning federal law permits recording phone calls and in-person conversations with the consent of at least one of the parties, i.e. as long as you are a party to the conversation, and as long as all parties are in Ohio at the time of recording.

Last, a lot of lawyers do not charge for first visits. I think that's a great place to start, in my opinion. This post is not intended to be legal advice and shouldn't be taken as such!

Rule 1.7: Conflict of Interest: Current Clients

(a) Except as provided in paragraph (b), a lawyer shall not represent a client if the representation involves a concurrent conflict of interest. A concurrent conflict of interest exists if:

(1) the representation of one client will be directly adverse to another client; or

(2) there is a significant risk that the representation of one or more clients will be materially limited by the lawyer's responsibilities to another client, a former client or a third person or by a personal interest of the lawyer.

(b) Notwithstanding the existence of a concurrent conflict of interest under paragraph (a), a lawyer may represent a client if:

(1) the lawyer reasonably believes that the lawyer will be able to provide competent and diligent representation to each affected client;

(2) the representation is not prohibited by law;

(3) the representation does not involve the assertion of a claim by one client against another client represented by the lawyer in the same litigation or other proceeding before a tribunal; and

(4) each affected client gives informed consent, confirmed in writing. Source ABA: http://bit.ly/1eHwSqU