For any type of family law, which this is about, then you want a lawyer who is in the (same) county/city of the court where the case is held, since that lawyer will be familiar with the judge on past rulings and the lawyer is known to them also in the court/judge.
Now all lawyers charge hourly fees (unless) it is a personal injury case. So for every hour they work on the case, be it phone calls, pleadings or motions and (court time) they will bill the client for their time.
So unknown the distance/time from Independence to Springfield? So, lets say that it takes 3 hours to drive to the court and 3 hours to drive back which totals to 6 hours, which you will be billed for (6) hours, since the lawyer charges you for their time. Now do you understand why told to hire a lawyer in Springfield vs Independence?
You don’t state if a court set up visitation in the past, or the reason for the mother taking away visitation, so only a real lawyer in person can tell if you need a lawyer or not.