You are not going to be on the same page with your co-parent on every issue.
House rules may differ across two different households. The children may eat different things in both households. They may wake up and go to sleep at different times.
The key is how you go about tackling those issues with sensitivity and care.
Particularly emotive issues like screen time, use of mobile phones, social media and boyfriend/girlfriends with teenagers probably warrant a discussion with the other parent ahead of time. If other children in the class are getting mobile phones, and your child has asked for one it is a good idea to chat the implications through with your co-parent. Children generally respond well to not having to be caught in the middle of two parents who cannot agree on a particular issue. Again, getting out ahead of these issues will be critical.
What you definitely do not want for your children is for them to be caused distress or emotional harm by your failure to compromise on simple issues such as these. If you can’t agree something, consider mediation or consulting an expert.
Do your children need to see a counsellor to talk about the issues? Many schools will offer that sort of service as an outlet for a child who is caught between their parents. There are some issues that are more important than others and you are going to need to know when to let go. You can’t govern everything that happens in the other household, but you can be respectful of the other parent and make observations without judgement and in the best interests of your children.
Courts are not the place to resolve disagreements about parenting styles. Judges simply do not have the time or inclination to resolve when your child should have an iPad or whether they should be allowed to do sleepovers with their friends. Mediation is the best place to start but there are also parenting coordinators who can adjudicate on any parenting decisions by mutual agreement.