I have advised many parents in this sort of conflict, on both "sides".
You have said you want to take the pressure off your child. As they are 12 they are old enough to express a preference but asking them to say if they want to stay the extra night at each visit, will be stressful. They may find having a written agreement easier, then the pressure is off the child to decide whether they want to stay. This is assuming they will be safe and looked after at either home.
If the relationship has generally been good, and your ex loves and looks after his child, then denying extra visitation will need to be justified.
Before you go to court you have to attempt mediation (or have a very good reason for not - like DV). It is cheaper, it will allow you to write a new contact plan and agree a review date. It will be more official feeling but unenforceable, so still have flexibility. A child contact order made in court, can be enforced.
If you still can't agree a plan with your ex then you might end up in court. CAFCASS may be asked to talk to you/ your ex and your child separately, to write a report and make recommendations to the judge. Ultimately if you and your ex can't agree then a judge will on your child's behalf.
childlawadvice.org.uk/information-pages/contact/
Child law advice can give free legal advice via email or phone, for family or child law the number is 0300 330 5480.
www.cafcass.gov.uk/grown-ups/parents-and-carers/divorce-and-separation/