Not dogwood. It is a bit out of focus and I can’t see how the leaves come off the stem, but perhaps Malus which includes apples and crab apples.

Thank you so much for answering. Very helpful to know that it is a Weigela. Winter temps were pretty normal here, not abnormally cold. We did have two abnormally deep snows, but otherwise the winter was relatively normally with average snow pack. I never use salt and when I shovel the stoop (which is near one shrub but not the other) I try to avoid dumping any of the snow onto the shrub and aim for the lawn or the Bishop Weed. I think our spring was warm earlier than normal, but temperatures seem pretty normal for this time of year, maybe even a bit cool for June. We live in a desert so we don't generally receive much rainfall, but I don't think we are in a drought this year. We have an automated sprinkler system and it runs 3x per week for about 15 minutes in each zone which is the same as we've done for the last 2 years. I do think we turned it on earlier than normal after our lawn started to show stress from the early warm spring. I will get in there and clear the Bishop Weed from around the plant. If it's that aggressive, I imagine I will have a very difficult time clearing it completely, but I'd be happy to work on keeping it back from the shrub. The previous owner seems to have planted it as ground cover in the two beds against the house on either side of the patio. After looking the plant up online, many of my neighbors have the variegated variety of Bishop Weed planted as well. I am always battling the variegated variety which creeps from my next door neighbor into my front flower beds. Is it ok to cut back the branches that lack leaves as we are going into summer? (Summer temps are typically about 90 during the day and can easily go into the 100s during July and August.)

Thanks for the advice! The mulberry shrub is already disposed of, and yes, I did notice the yellow roots! We were planning to move this year ( which got delayed ) hence the plant in the pot, for the new place. Yes it self seeds here as the soil under this shrub allows it. However at my mom's place her rose of sharon was on the front lawn surrounded by grass, never an issue with self seeding and spreading. That's the any way to go in future.

Unfortunately I didn't the option to add any photos to my original post. It (the option add photos) only showed up now in my reply.