You mention a vinyl floor. Do you mean laminate? Or is it in the bathroom and I am not seeing it? What color and what did you have in mind for a replacement?
Also having trouble with the flow of things. Could you do a quick floorplan sketch? Doesn't have to be fancy. If you want to do something more formal, Sweet Home 3d is free open source software. It's great and with a quick learning curve. You will find having a scaled drawing of your space will come in handy when ordering materials like new flooring, paint, etc.
It looks like you have enough light to pull off deep blue-violets or purples in the dining room if you want but before I make suggestions I want to see how traffic and the eyes of people flow from room to room. Most of my love for color and years learning it formally come from my Mom. She put together stunning rooms anchored in deep regal purples. Lavender doesn't float my boat so much. It has its place but usually strikes me as a little too fififoofoo.
Not sure how to comment on color for the bath until I see where it is. People are afraid of dark colors in baths usually because the lighting sucks. And too much color reflects and tosses off the women folk that like to fard in them. Tell me what you have?
It's funny, my color reference books have been sitting for ages and all of the sudden, thanks to this site, I seem to be dusting them off. Anyhow, here is a page from one of my fave references, "Color Harmony Workbook" (sadly I think it is out of print). Is something like this along the lines of what you had in mind for your dining room? It is a simple and elegant color scheme. Your existing BRIGHT WHITE woodwork in that space would have to be toned down but I can adjust the scheme to work with your existing carpeting on the stairs. I've got some time on my hands so can play a bit. Perhaps it will help or inspire others on this site to do the same.