Disillusioned with the local bike shop

I got my wife an old bike at  a garage sale over the weekend, a 15 speed Murray mountain bike built back in 95. Sure, it has the cheap type of construction on the frame, but it looked like the frame was in great shape. $15 seemed reasonable, of course, I had to buy new tubes and brakes, adjust the rear derailleur, and tighten the kick stand. I did a few test rides on it to make sure it all rides ok, and it is a smooth ride. Much smoother than I expected. Smooth enough that if I didn't have dangley  bits, I would be happy to ride that thing around town.

Next to my mtn bike, in the 'garage'

The only 'problem' I have with the bike is the rear brakes. They don't seem to have the grip that I like, but I can't figure out if I am just being paranoid, or if there is some issue I am overlooking in the 7 or 8 times I have tried to adjust them over the last few days.

I have a theory, in that the rear brake cable is coming from the bottom, instead of the top.

Right now, that is my only idea on why I can't get the brakes as tight as I want them.  My wife thinks they are fine, but I am not convinced she could stop on an incline using the rear brakes. Oh, the front brakes are nice, but the rear ones are driving me insane.

I decided to take it up to the local bike shop, and at least see if they could tell me if I was being paranoid, or if there was a glaring error that I just kept missing, like perhaps the damn wire is in wrong. The only thing they would tell me was that could do a full adjustment to the rear brake, for somewhere between $10 and $15 bucks depending on what it needs done, and it would be ready in a few days. I decided to take it home and keep fiddling with it. The problem with leaving it was two-fold. 1, I hadn't messed with it enough to get frustrated enough that I thought 15 bucks and a few days at the shop was worth it yet. 2, it seemed pretty likely that the only answer I would get in a few days was 'they needed adjusted' and that sure as hell wouldn't help me understand what I was missing. (Unless the cable came back reversed, and then I would be miffed that they couldn't just say, "hey, your cable is upside down" (it was like that when I got it, but then again, it didn't seem to have been ridden much)

Look, I understand that part of the function of the Bike Shop is to make money. This year, it has made its fair share from me. I had my mountain bike serviced this spring, when I got new tires, tubes, pedals, and had them double check the gear settings. It cost me nearly $100, mostly because of the gears, which were ok, but they charged me $40 to check that. (I really think they screwed me there, but I guess I should have been more specific when telling them what I wanted regarding that.) I  also picked up another set of pedals for my hybrid bike (not quite skinny tires, but not mountain bike tires either.) but this time I installed them myself.

I don't expect the bike shop to bend over backwards and move my problems ahead of the line. I really don't. But I do expect them to at least say 'yeah, the brakes don't seem right' or 'they seem ok, but we can double check them' without having to pay ten bucks and wait a few days. I am not asking to have a wheel trued. I just want a second opinion on if the brakes seem ok, because they seem weak to me.  (Being fair, my two bikes have a different brake system, and that alone might be why they seem odd to me.)

I might try this week to reverse the entry point of the brake cable, and see if that works better, otherwise...  I might just take it to an out of town bike shop. I'm still a little ticked at the local one.