What if a tenant's kid for whatever reason makes their way inside the fence and god forbid gets injured by one of the dogs?

So, for example, if you personally had knowledge of a loose step in one of your properties and didn't fix it and then your tenant was injured on it, even though the property is held in the LLC, since you had actual notice of the dangerous condition you could still be held personally liable for the tenant's injury.

You need to verify this as well.If someone has a 'helper' on your property (and no WC) and they fall and injure themselves, then you will get sued for damages.

If someone injures themselves and sues, they will be suing the LLC and not you personally.

What happens if the Tenant is injured while working on the property and decides to sue?

The people doing the Maintenance work could be considered employees if injured or get sick due to the work. 

I was injured playing football back in 2011, as a result I started a storm restoration company and a yacht rental company in Florida.

You should get coverage for the units under the LLC to cover:1, The LLC's Liability if someone is injured in the unit (legal costs and judgement if any)2.

Besides, If I wind up in the hospital for the foot I've injured due to their negligence for a third time, I dont even know what I can do.

Worse yet, if someone is in a super difficult situation, injured in the mountains and needs a helicopter ambulance, they'll be looking at a bill of $20,000 or more!