What could have made a satellite appear to move side to side while near the horizon?
Your link shows estimated magnitude, and it gets quite dim when it gets close to the horizon. 



above: from heavens-above, (from url: lat=52.2681&amp;lng=-113.8112)

As a spacecraft in low earth orbit appears to approach the horizon, the line-of-sight distance from it to you can change from a few hundred to a few thousands kilometers, which is why the brightness in your table changes so much.

The path in the sky shown in the link is going to be almost vertical (reaches 70 degrees). Wikipedia says GEOS-3 is a satellite put into orbit in 1975. These days there is a big effort to de-orbit the "leftovers" so they burn up in the atmosphere (space junk mitigation) but back then it was common for each launch to leave other stuff up there for decades or longer. 

Wikipedia says the COSPAR-ID for the actual GOES-3 satellite is 1975-027A. That means it was the 27th internationally recognized launch in 1975. "A" is assigned to the GEOS-3 satellite itself, but if you look up 1975-027 in the satellite catalog (SatCat) at Celestrak.org you can see there are were four other objects associated with the launch being tracked. One of them has burned up, but the others are still there.

You can double check if 1975-027B is the one that your link is talking about. Anyway, since they are so old, none of them is capable of a spectacularly sudden engine burn and change in orbit. So I'd have to say that whatever you did see, it isn't associated with the GEOS-3 launch.

Another point to consider; if you just coming out of a restaurant, the chances are low that you could see a 5th magnitude object. Near the horizon the apparent speed would be much slower than that of a satellite overhead.