I don't know your back story or your reasons for not wanting your childrens father to have reasonable access to them.
I'm divorced from my XH. He walked out when they were 1 and 3 stating parenting wasn't for him. Turns out he'd been having an affair and moved straight into another womens bed. Our elder son is also severely disabled. Then less than a year later I got a solicitors letter saying I was blocking access.
There are many ways access can go but court is a very expensive process - financial, emotional and it can have quite a profound effect on everyones relationships.
The long and short is that having had children together you have a tie which is going to go on for every remaining child related event of your lives.
This doesn't suddenly stop at 16. There are things like graduations, weddings, grandchildren coming along where you may well need to be able to be civil for your childrens sake.
Quite common shared access arrangements appears to be one night in the week and every other weekend. You don't need to be a doormat and do things to suit your XH but you do need to consider what is in the childrens interests and how could the situation work for all of you.
I don't claim to have found the perfect solution but my XH does things like take our younger out for a kick about at the park, they go off road biking together (something I don't really fancy). He takes the older one out to Ikea restaurant for tea (when we were allowed to). Its things the children enjoy but to a timetable that works for our family.
We communicate by email to keep all arrangements in writing and at first I only accessed the XH email folder once a week to limit my exposure.
So are there any mitigating circumstances that leave you very concerned about more access?