What they wrote is fairly reasonable. What do you expect from renters? They are renters, ofetn people who can not afford to own a property, period.
Now here are the facts: large, low (but consistent) income family, more than average wear and tear, small-to-medium pet...
If you are not comfortable, don't rent. You are the master.
Do not explan in writing in length to tenant directly. The more you explain it, the worse.
On the other hand, unless your family intends to move back to the same house later, what does "我们有过敏" has to do with tenants having pets? Many tenants have pets. You charged pet rent, deposit, that will be fair.
Not allowing pets will limit your renter pool.
