With 2 small kids, our current setup is totally insufficient.

If they do give notice and they're great tenants with a special circumstance, like a job offer out-of-state, I have been known to just let them give insufficient notice, but I have everyone sign an early termination addendum, something like, Tenant agrees to vacate no later than x date.  

Depends on whether you have a true due diligence period or just an inspection period in the contract, but I absolutely agree with you generally that the language included is insufficient and that you should have something to the effect that you can terminate in the event that the leases are not acceptable, or the tenants are not current on the leases and request not only the leases but also confirmation of the tenants being on time and in compliance with all terms. 

The tenant just paid his April rent and low and behold, it came back insufficient funds, so the 5 day notice will be mailed soon.

I do use cozy for payment processing and have auto payment set up but many times the payment fails due to insufficient funds.

I am waiting to see if I can get any details regarding the bankruptcy, specifically if it was one incident or multiple that lead to insufficient funds in the account.

I've got some others that focus on sleep and nutrition, but the three listed are what I'm attempting for business betterment.

I figured if I could understand how people model the purchase of land without income I could then model houses with good land value but insufficient rental income.

My bank tried to auto debit ( Cozy) his account on Jan 5th, 5 days past the rent due date and it was insufficient.

Finally, with the use of Trusts while establishing these structures you can add a level of anonymity by removing your name from public record.I want to also add that you can create these structures and operate them insufficiently, mitigating their protection.