I think it's a great idea NDDT. As long as you are comfortable that this lawyer can still be unbiased. My STBX and I are also using a mediator. At first she wanted to use her friend's mother for that which I said no to. Obviously serious concerns about her ability to not show some type of bias in the situation. So depending on how much time she has had with him, etc....you may want consider that.
Otherwise I think Mediation is a great idea. Once you have an attorney representing you...IMHO...is when it gets ugly. If you two can come to terms on your own...you will be way better off. It will help you in whatever R you two have in the future (co-parents) and it will most likely save a lot of money.