Answer: Based on your description I think you may have a Japanese maple (Acer palmatum) with red foliage rather than a run of the mill red maple (Acer rubrum).
If this is a Japanese maple, it is probably a fairly valuable specimen tree that is well established and has been growing nicely. In my experience it would probably be better to leave it alone and move the shrubs, since shrubs are less expensive and more easily replaced if the transplanting fails.
If you truly want to move it, you should probably root prune it beginning a year ahead of the move and then dig and move it either in late fall or very early spring just as soon as the ground can be worked and while it is dormant. Without root pruning, the roots will be wider than the branches, and it is important to take as many of the roots as possible when you dig it up. This means an extremely heavy root ball.
You might need professional equipment to move it, depending on how far it has to be moved for replanting. Also, you would want to replant it in a location very similar to where it is now to reduce the chance of shocking it. It should be replanted immediately at the same depth as it grew before; the new hole should be wider than the roots, about twice as wide, and about as deep. Do not plant it deeper or allow it to settle lower than it grew before as this will kill it.
And of course, after the move you need to water it to keep the soil evenly moist (but not saturated/sopping wet) any time it is not frozen for at the least a year or two while it reestablishes.
I would suggest you consult on site with a professionally trained and certified arborist if you want to go through with moving it. They will be able to explain the root pruning process and also how to go about moving it and help you judge the best time to do the job. Good luck with your tree!
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