From my understanding, insurance won’t cover a dead tree falling as this is a result of “neglect” but would my current dwellings insurance cover it under personal liability?

Does the tenant's liability insurance kick in if there is damage caused due to their negligence? 

@Catherine Javier If you find the property is more of a liability to you and ultimately decide to sell, the 1031 exchange would probably be the best way to take advantage of using the tax and find something with a greater growth potential.

Your WY LLC can be beneficiary of the trust, giving whatever liability protection that offers.

By this I mean the liability event that has you so concerned. 

But many landlords are reluctant because frankly real estate and renting is fraught with many problems and liabilities.

I just have vacant home insurance along with regular home insurance, but no other professional liability insurance.

Limiting issues and liability is the goal.

It also becomes more difficult to separate out construction related liability when there's one partner who is responsible for the construction management. 

I would also note your mention of not wanting liability, but offering to "co-sign".