How about a perennial groundcover of Geranium maccrorrhizum or G. 'Bikovo' or G. 'Karmina'? It would be in bloom now.

Both spots look like they have plenty of shade — I’d try impatiens. They require no maintenance beyond watering and they’ll bloom until the frost kills them.

For annuals -- wax begonias or impatiens. I don't think the impatiens will do well under the tree because the soil is likely too dry, but in the other area they may be fine.

Your vinca probably never got full and lush because they like it sunny, hot, and not too moist -- you've probably got too much shade for them to truly thrive. Salvia will tolerate part-shade but is better in full sun.

The tree is planted way too close to the sidewalk. Boy, is that awkward! Was the sidewalk just replaced? It looks much newer than the house. Our 20 year old neighborhood has maples planted in every parking strip and the roots are pushing up all the sidewalks now.

You need a tree on the corner of your house, not there. Bite the bullet and get out the chain saw.