Translation:My mother wants a house on the coast.
I can't think of a sentence where "ved" means "near". Either I'm just tired, or it shouldn't suggest that translation. "Ved" is hard to explain - it has many meanings, but as a preposition it mainly means "at" or "by":
Manden er ved træet = The man is at/by the tree
Jeg er ved bilen = I'm at/by the car
If you say "ved siden af" it means "next to" (literally "at the side of"):
Jeg står ved siden af bordet = I stand next to the table
De to venner sidder ved siden af hinanden = The two friends sit next to eachother
I think it can be confusing that this sentence translates "ved kysten" as "on the coast" because most of the time "on" is translated as "på" in Danish:
Han står på mig = He's standing on me
Han er på stranden = He's on the beach
Jeg er på flugt = I'm on the run
Jeg spiste frugt på min fødselsdag = I ate fruit on my birthday
(Sorry that I ended up writing so much, I hope it helped a little!)
Almost, but I visualise 2 distict images when I hear the 2 phrases. If I ask someone their location and they say , "I'm by the car", I'm assuming they are next to it e.g. pretty much within kicking distance. If they say "I'm near the car" then I'm assuming they are close but certainly not next to it e.g. they could walk to it in within a minute. Not sure how this relates to 'ved' though.