You can remove the suckers whenever you want to. It will not affect the flowering of the rest of the tree. You can make "thinning" cuts whenever you need to. Thinning means to remove a whole branch or limb to where it meets another main branch or trunk. The rest of the intact branches will flower normally. If you make "heading back" cuts this means you cut a branch near the end of the branch or halfway. This will remove any current or forming flower buds, and will generally cause the plant to "bush out" or make a bunch of new growth where you cut. It sounds like you need to make thinning cuts and remove suckers. Go ahead. I do this all the time to let air and light in but I don't "whack off" any crape myrtle branches.
Laurie