Rhododendrons and azaleas have shallow roots and need moisture but good drainage. It sounds like a poor match. Also, soil near a foundation tends to get alkaline from the lime in the concrete. Rhododendrons and azaleas need acidic soil. Also rhododendrons and azaleas each bloom only about 2 to 4 weeks each spring. You can plant to get 3 months of bloom, but not from one plant. Here are some drought tolerant flowering shrubs. Glossy abelia (Abelia x grandiflora) is a drought tolerant, semi-evergreen shrub that has a moderate growth rate and spreading habit that is dense and rounded, according to the North Carolina State University. It grows 3 to 6 feet tall and wide and produces white, funnel-shaped flowers that bloom along the arching branches. These blooms emerge in early summer when temperatures are often high, and the ability to withstand drought is ideal. As they grow, the slightly fragrant blooms develop a purple and pink tinge to create a striking display. Abelia bears glossy, dark green leaves that cast a bronze-green to red tinge in winter. The shrub tolerates clay, dry and damp soils; grows best in full sun to part shade and well-drained soil; and responds well to severe pruning. Grow glossy abelia in U.S. Department of Agriculture plant hardiness zones 6 to 9. Caryopteris x clandonensis 'Longwood Blue' is a drought tolerant deciduous shrub with a low, mounding habit and moderate growth rate, according to the Missouri Botanical Garden. It grows 3 to 6 feet tall and wide and has a spreading growth habit. It produces flowers that resemble clouds of blue smoke, hence it's common name, blue mist. The fragrant, violet to blue flowers appear in clusters or cymes from late summer into fall. Blue mist is not only drought tolerant, but also heat tolerant, ideal when the late summer temperatures creep up and moisture is limited. The silver and gray, ovate to lance-shaped foliage on blue mist is aromatic. It grows best in full sun and well-drained, loamy soil in zones 6 to 9. It is not tolerant of wet or poorly-drained soil. Wintergreen barberry (Berberis julianae) is a slow-growing evergreen shrub that has a rounded, dense form that becomes more open with age. It grows 4 to 6 feet tall and 6 to 8 feet wide. It produces small, yellow flowers that are abundant in April and May. Following the wintergreen barberry flowers are the blue and black fruit that persists into fall. The dark green, 2- to 3-inch-long foliage on wintergreen barberry is serrated, and in fall, turns a stunning wine to red color. Wintergreen barberry is the hardiest evergreen barberry, according to North Carolina State University Extension. It is drought tolerant and grows best in full sun to part shade. Wintergreen barberry tolerates a wide range of soil types. Grow wintergreen barberry in zones 6 to 8 Here is a link that might be useful: Drought Tolerant Shrubs (not all bloom, some are deciduous)

I'd think the evergreen rhododendrons would be more likely to get burned than the deciduous one. While both of these particular ones are subzero hardy, generally the deciduous habit is associated with winter conditions (except for deciduous tropicals, that defoliate because of seasonal drought or flooding) that are too severe for broadleaf evergreen foliage. Here on the west coast native broadleaf evergreens are few in number in the PNW, but as soon as you get into Californian conditions (milder winters) in southern Oregon the broadleaf evergreens start to really give the conifers a run for their money, resulting in the 'mixed evergreen forest'.

The first thing to do - and I do not mean this in any sort of unkind way - is to learn the identity of what you have growing so that they are more definite than just trees and bushes. This would also prevent the inadvertent destruction of something valuable and help guide decisions about placement. As for the rhododendron and azaleas, much is a matter of personal taste. The azaleas especially will respond quickly to even radical pruning and you will lose only a year or two of bloom. They are also one of the few types of shrub that can grow close to a foundation without any worries about invasive roots. For all of them, why not wait a year or so and see how they respond to the increased light brought about by the tree removal. Azaleas and rhododendrons are among the easiest plants to move even when quite large so there is no real reason to do it immediately. If, on the other hand, you have a clear vision of what you want - and this does not seem to be a shady woodland type garden - then remove them. It's your property to do with as you wish.

In somewhat random order: salt (especially) and heavy snow can severely damage rhododendrons. Locations exposed to winter sun and wind will be a trial for almost all rhododendrons. Early, medium or late designation is about the best you can hope for as a guide to bloom time, but many factors are involved. Even slow growing so-called dwarf rhododendrons will eventually exceed four feet in height. You need to decide what kind of rhododendrons you want. Large leafed (elepidotes).? Small leaved (lepidotes)? Deciduous? Evergreen? Then take a trip to a good local nursery to see what's available. Given what's happened in the horticulture industry over the last couple of decades, the selection will be limited. Mail order sources will have more choices. In all honesty, your proposed planting area sounds pretty far from ideal for rhododendrons. You might be much happier with a different genus of plants.