"they have done things at the property without my permission"
Cure or quit notices need to be delivered at the time of the violation. In court, a lack of response can indicate the landlord is fine with the situation.
"trampoline" Trampoline needs to go. Cure or quit *immediately*.
"They are a nice family" "The tenant is a low-quality untrustworthy person"
Which is it? This is starting to sound personal rather than professional.
"a remedy that balances discipline and peace." The tenant is your customer, not your child. You don't *discipline* your tenant, you post notices in accordance with your state laws. Why haven't you done that with the previous violations?
"reminding them of where they stand in the landlord/tenant hierarchy." This one statement shows something about you as the landlord. You have legal recourse to solve your problems, and you're more concerned about being in charge as the "lord of the land" holding it over your tenants.
Here's the actual hierarchy - Landlord and tenant have a legal agreement in place. This is so neither is "higher" in the food chain than the other. There are also laws in place to prevent either party from taking advantage of the other.
Unless an issue is as safety issue, at this point you should let it go and do any repairs after the tenant leaves. Do not renew their lease in 8 months.
You also need to check your business-owner mindset. A landlord who thinks like you do (that they are "superior" to their tenants, their customers) will treat good and bad tenants this way. You're going to make some sort of mistake, most likely with the handling of the tenant's security deposit, because of your sense of entitlement. It will cost you.