Hi,
You really have to start putting your child's needs above your own, and so far you haven't been. You are obviously a very loving mother, but so far it's been in a possessive way that is wanting what's best for you, not the child.
I'm sure your ex was a knob to you. That doesn't mean he can't be a good father. Your child has the right to a normal relationship with their Dad, and by doing everything you can to sabotage this, you are putting yourself at risk of a family court decision that you won't like.
- it was very wrong to badmouth him to your child, saying he broke your heart. It's true, but inappropriate to put that on a child, and the only reason to do that was to turn your child against him. Parental alienation is not tolerated by the court. Moreover, it's going to hurt your child. It's failing to recognise your child's needs for a good relationship with their father. It was selfish of you. Your child's feelings are more important than yours
- not permitting unsupervised access because you want to be with your child 24/7. Again this is about you, not your child's best interests
- Not putting the father on the birth certificate to have a 'lever' to use on the father, again your own wants put over your child's best interests.
You are not being a good mother when you do things like these.
Risk of flight to N Ireland - there doesn't seem to be strong evidence of this, but the court will help you by ruling in who the child lives with and access arrangements. You need to be reasonable, as does he. Weekends and weekdays can and should be shared fairly, for the child's not parents' benefit. You need to argue for what is best for the child, rather than what you want for yourself, to show you can put your child's needs first. So if you want every other weekend, state why that is best for the child, not why it is best for you.
Inaccurate report - it sounds as though there are inaccuracies in either your or the father's criminal record, so yes, the police are the only ones who can change that. The family court can only go by what the police record shows, so get it corrected ASAP.
The tape - if you believe it has recorded sexual activity while the child is present, you need to go to the police. If you have, and they are not hearing what you hear when they investigated, then you need to let it go. If you haven't taken it to the police, than maybe deep down you know you are mistaken.
I know the pain of being cheated on, but you are letting your anger negatively affect your child, and are risking being in a worse position regarding access/residency.