Question about our willow

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

Another view

Last photo...another angle. I'll have to get a better photo of the cavity when I get home as it came out blurry as all get out.

It's the nature of most willows to grow fast and then start falling apart at a relatively young age, 50-60 years sounds about right. It may not die anytime soon, but it probably will continue to drop limbs every now and then. At the very least, you should start planning for its replacement.

Hi Erynne! We have many large (mature) willows growing around our pond. Some of them have survived with split trunks, and they all drop limbs willy-nilly in windy weather. The one nearest our house was cut down a few years ago, and it has sent up new branches from the stump, so even felling them doesn't get rid of them! I guess you'd have to grind the stump down to the ground.

Thanks for your input! I'm going to be getting as many quotes as possible to have this tree removed whether my husband likes it or not! It's obviously getting to a really mature stage as another branch came down last night. You're right June about the wind; always a mess afterwards. I had silver maples at my previous address and I thought those were bad but these willows seem to be worse! At the least, living with these two types of trees has taught me what not to plant! I want to fill this place up with trees, shrubs and conifers to cast some shade for future gardens but it's all seems quite daunting and I fear making poor choices over the long term.

Cheers,
Erynne