Trees, Shrubs and Conifers: Question about our willow, 1 by Erynne

Erynne wrote:
This willow is on the far end of our 1 acre property and there is another just like it on the opposite side of our yard. I'm guessing that it's quite up there in age because a 51 yr resident of the area said the willows have been here as long as he can remember. We've been here just over a year.
About 3 yrs ago a large limb came down. As a result, there is a cavity on the trunk about 5' up and a little below the crotch. The cavity measures 9" in diameter with a piece of the old limb still filling less than half of the one side of the hole.

So question. How much can a cavity like this weaken an old willow? Branches are constantly falling from this beast and I was nearly dinged in the head by a good-sized one as I was riding by on the mower. I won't go near this tree now. Husband loves this tree but I'm afraid of it...Ha!
The other willow appears to be in good shape at the moment and the amount of branches falling is neglible. Another odd thing I noticed is that there are wild strawberry plants growing in the crotch as well as another species of tree!

I have been phoning around for an arborist but I'm having a tough time finding anyone who will come out here as it's "not in their service area". The only company nearby that does tree maintenance doesn't have a certified arborist and they are reluctant to deal with willows like this.

I guess I need to know the likelihood of this tree falling down. We have four children and a pup so I'm rather nervous.

Tks,
Erynne