I’ve made a mistake; planted the tree in the sun. It’s growing but leaves of course look lightly burnt. We live in Michigan.
You are very lucky to have a tri-coloured beech or Fagus sylvatica ‘Tricolor’. I too have one and I just adore its foliage. From the research I have done, many nurseries will say to plant this tree in full sunlight and some say part shade. I have mine in a south facing backyard in the fullest sunniest spot possible. From my experience, having good soil mixed with plenty of compost and a regular watering schedule is the trick to growing this tree in a sunny location. When watering, ensure you are watering at root level and not wetting the leaves themselves as this could cause burning in the hot sun. If you are able to do this, you should find that your leaves remain the beautiful pink, purple and white they should be (although colour does vary slightly from tree to tree). You could also add a couple of inches of mulch around its base ensuring that it does not touch the trunk itself. The mulch will further help keep the moisture in with the added bonus of keeping the weeds out.
If you do feel the need to move the tree, depending on its age it is possible to do so. Again, I speak from experience as I had to move a tri-colour tree for a client who was doing a renovation. You will want to ensure you get as many of the roots as possible and water it in well. This is something to really consider as these trees can live to 100+ years in the right conditions.
For further information on your tree, please see https://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?taxonid=254956&isprofile=0&