And a far away shot.

Something between a small partial trunk shot - that happens to also show some leaves - and a distant view is needed to get a clear picture of what is involved. But otherwise so far what it looks like is a weeping Japanese cherry (Prunus pendula) grafted onto a birch-bark cherry (P. serrula) trunk (inter-stem), that apparently was itself grafted onto a sweet cherry (P. avium) root-stock. Which has been allowed to grow its own trunk(s) up next to the birch-bark trunk, make its own top above the weeping cherry + birch-bark cherry combination.

What needs to be done to save the specimen is saw off the sweet cherry top where it originates, probably at ground level. It is big enough now that it will have to be cut down in sections, starting well above the crown of the weeping cherry.

Thank you so much for the ID. Here is another photo showing the schism! Left side has branching in all directions, right side reaches for the sky. Below this the trunk looks like all the same tree. Leaves look the same on both halves.

Location is perfect for a shade tree. Instead of trying to rehabilitate this one, should I remove it and start over? July in Sacramento is not the time to plant. I have a couple of months to consider something different.

In this last view looks like weeping cherry grafted on top of a sweet cherry trunk (and roots), with the sweet cherry having sprouted a second trunk which has grown up through and above the crown of the weeping cherry.

If you don't want the weeping cherry then - yes - cut the whole thing down and take it out.

If you're new to the house you won't have seen it in flower. How about giving it one spring to show you what it looks like in bloom? Then you can make a decision on whether to remove part or all of it. You may even like its quirky peculiarities when it's producing two different flower shades.

If retained the sweet cherry sprout will eventually replace the weeping cherry. And already the effect created by letting the stock throw up its own top is ugly, even monstrous.

I think it's up to the OP to decide if it's monstrous. Or whether removing one part would suffice.

I think it's up to the OP to decide if it's monstrous

This position offers no horticultural insight. Apart from the aesthetic considerations involved since the sprout from the sweet cherry trunk is a reiteration it may perfectly well tear away from the trunk at some point if left to grow ever larger and heavier.

And somebody paid at one time the cost of buying a grafted weeping cherry. To now let the sweet cherry stock continue spoiling the original grafted combination throws away this original investment - a sweet cherry with a kink in it bursting through a weeping cherry top is not the best case scenario here.

Anyway original poster has already referred to the existing situation as a "schism", stated that they want a shade tree in that spot. The sweet cherry is likely to keep trying to make its own top indefinitely, since the weeping cherry will not be as large growing as is wanted there is no point in trying to maintain the grafted specimen. The best thing would be to instead remove the combination and replace it with a more typical shade tree. One that will develop a broader and more attractive canopy more quickly.

https://www.sactree.com/trees

I read

Location is perfect for a shade tree

as being "this thing doesn't look like what I want in this spot".

Even if the weeping cherry is cut off and the replacement sweet cherry top retained for its existing and potential size there is still the problem of how the crook in the trunk would look, as well as the possible mechanical failure (tearing away of the reiteration). And the fact that the sweet cherry will never make a nice lush shade tree. But will be likely to start producing fruits. Ones that might in this instance be seen as a nuisance rather than an enhancement.

personally, I'd be inclined to start over, the weeping part doesn't look very balanced (to me).