Attempts to seek suggests you have a MIAM. You send the ex a message saying you have commenced mediation and she will be invited to attend and will hear from the mediator in this regard. The mediator contacts the ex to ask her to attend. The Mother doesn't attend and you get signed off.
You then have the email to prove you attempted to seek mediation - not that you can submit that as evidence with a C100 but you can say you started mediation and the Mother was invited by both you and the mediator, in writing, but declined to attend. Then it shows you tried. And you'll be believed because you can prove it as and when evidence can be shown and she can't prove otherwise.
But - if the Mother does attend - and the first session is bad (as expected) - a mediator might then say they want you to try three sessions. As you say she isn't going to want to spend the money. She might do what mine used to do "yes I'll go to mediation if you pay for it".