Don't prune it in bloom, there's a good chap.
The branch that splits off from the main trunk should've been trimmed before it grew out. Can be done, later in the year.
Your ornamental cherry tree, seems to be 'Cheals Weeping' an attractive tree when in full flower. It will have been grafted onto a wild cherry tree root stock, that bears little in the way of flowers, The upright branch is the wild part and needs to be removed. Carefully cut it out now or when the main tree has finished flowering, as 'Odds' has suggested.
Trees such as Prunus sp, which are prone to silver leaf disease are best pruned from April to July when the disease spores are not on the wind, and the tree ...
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