Just going through the pieces of information you've given so far.
1.
At GF's house the laptop gets speed tests of perhaps 17megs or better.
This tells me that your laptop wireless hardware and drivers are fine.
Speed test sitting here prior to writing this at GF's comes in at 18megs
2. Hard wired my laptop into the router and also got 3 megs.
This tells me that the problem is not in Frontier's network. It also points me to a problem in the router's wireless settings or interference with a neighbor's router. I'd look for one of the free stumbler utilities and do a scan of available wireless networks around your shop. If your neighbor's router is using channel 6, I'd change your router to use channel 1 or 11. The stumbler utility should also show you the signal strength that is coming off your router, which should help with #6.
Will look into this. There are only two neighbors at the shop (three counting the Frontier switching building next to the shop) but none of them ever appear as an available network on the laptop in the office. Occasionally if I am at the far end of the building I will get one neighbor popping up on my phone.
3. Have run several scans with Spybot Search and Destroy, AVG, and so on all coming up clean.
Doesn't sound like a malware problem to me given that the laptop performs well when cabled to the router and while at your GF's house.
4. Galaxy S5 consistently shows 3megs or better.
Was the Galaxy using the cellular network or WiFi from router and in the same location? If the Galaxy was not using the cellular network and you did the speed test from the same location as the laptop, I would look at the MTU parameter in the TCP settings for the wireless network adapter, and match that to the MTU setting in your router. The default MTU size for Windows is 1500, but if the laptop's MTU setting exceeds the MTU setting for the network, performance will degrade as every TCP packet will have to be split. I assume that the MTU setting in your router's Ethernet settings is compatible with Frontier's network, since you are getting good performance there. Try a setting less than 1500 in your laptop wireless adapter settings (maybe 1365 as a test) and see if performance increases.
When I did the speed tests with the Galaxy I shut off cellular data thinking it would test across the wireless connection. My thought was if it was an intermittent issue with frontier I may have never seen it via the phone because normally my cellular data is on and I have smart switch enabled which I assumed causes the phone to optimize data from the best source.
Will do on the MTU as soon as I get to the shop.
5. Changed the SSID on the modem/router and setting up a new location on the computer and nothing changed.
SSID doesn't effect performance. It is just a way to identify the wireless network.
Just a monkey beating on a transmission with a whiffle ball bat attempt at a fix
6. Connection (my shop) periodically drops off the available wireless connections list. At just a few seconds ago the shop connection popped back up but say "the capabilities of your network adapter do not match the requirements of this network".
Would like to dig here a little more. Where is the router in relation to the laptop? I can't tell from your note whether the router is in the shop or a different part of the house. What would you judge the distance to be? How does this differ on the relationship between the router and the laptop when you're at your GF's house? I ask because your laptop Wi-Fi antenna might be limited. You could be at max distance or the signal might be weakened enough as it passes through building materials. You might also check router's antenna configuration for problems. I find that if a router is placed on a higher floor and nearly overhead, the antenna is not optimal to broadcast in that direction. Depends on the router. Look for that stumbler utility and see what the signal strength is from the laptop (and if possible see if there is a utility for the Galaxy).
The shop is a commercial building, the router is in the front office room which is where the laptop/desk is at the moment. Same room, 15' apart, no obstructions. At GF's its a small house, laptop works anywhere in the house, second floor, first, outside, router/modem is in kitchen. Separated by a wall or two and a single floor at most.
Last, Matt is correct that a 802.11b device will slow all devices on a 802.11g network. However, 802.11b is rated at 11 Mb, which is still faster than the 3 Mb you're trying to achieve.
Dave