Quiet Enjoyment of Property
I know that the term "Quiet Enjoyment" of one's property is a very loose term that describes the ability of a person to enjoy their private property and not be subject to unwanted nuisances and distractionsby their neighbors. Does any one have any concepts of what defines normal activities from nuisance activities? Can activities by children be considered a nuisance or do they have to meet a different standard than adults? Your answers may help in a pending court action.
"Quiet enjoyment" in US/UK common law is not about noise - it's mostly about direct interference from landlords and other authorities. If the children in question are directing activities toward you - taunting or trespassing, then you may have a cause of action. If they're just being extraordinarily noisy, you're probably out of luck, unless they're violating a local noise ordinance - which usually will specify quiet hours at night, and permissible decibel levels (which they couldn't exceed without amplification.)
Since your legal remedies are likely to be limited - and because neighbor lawsuits tend to produce ongoing grudge matches that reduce quality of life for all involved, you might consider trying to solve this outside of court. Consider contacting:
Solve it! Community Mediation Service (in Mesa, serving Greater Phoenix)
https://mywebport.org/published/l/ea/leadership/home/5/
Mediation can work even if you and the neighbors are not on speaking terms. You contact the mediation center, then they contact the neighbors, briefly laying out your concern and asking them if they'd be willing to mediate it. The mediators will be sure everybody stays on their best behavior during the discussion. The mediators do not decide anything for you - any agreement is between you and the neighbors, witnessed by the mediators, who can write it down for you.
I volunteer for a similar agency here, and it's always much better than a court ruling when a neighbor dispute can be resolved this way. You can get results that a court could not order or enforce - anything you and the neighbors decide, whether required by law or not. If it doesn't work, you've lost very little, and strengthened your case, if anything, by demonstrating the will to work it out.