Answer: Unfortunately, based on your description I am not exactly certain which shrub you have. Most of the spring bloomers (such as the white flowered old fashioned spireas, which I suspect this may be) are best pruned right after they bloom. The reason for this is they bloom on old wood so trimming in late winter or spring -- although ok to do -- will remove the flower buds and reduce or eliminate this spring's flowers.
Your crab apple tree sounds like it may have seen better days. Splits can be dangerous in that they can cause the tree to break apart in a storm, or make it weak enough that it just breaks one day for no apparent reason. Rotting is also not a good sign as it can also be decaying inside the tree -- but look ok from the outside. This can also potentially cause the tree to break apart and be dangerous.
Sometimes the tree can be pruned back to good wood and salvaged, but sometimes it is better to remove the tree and replant. I don't like to suggest that without having seen the tree. For this situation I would suggest you consult with a professionally trained and certified arborist who can make a site visit and examine the tree. If the tree can be saved they will be able to tell you that and what would need to be done for it, if not, they can explain why and show you why and then safely remove it for you. While they are there to look at the tree, they might be able to identify your shrub for you as well. I hope this helps.
Q&A Library Searching Tips