+1.
The rim definitely appears to be for a "front" hub. "front" being the "universal" term for a very small diameter hub with disc brakes fitted which is common. Your front hub is a lot more like drum brake diameter, so the angle is way off. Ideally, you would machine the holes for the spokes to fit the hub you have, but building spoke wheels properly is becoming a lot less common than it used to be, and we have a lot of universal rims being sold. Bicycle guys are great, but they really do not see this as their biggest hub is super tiny compared to the rim diameter, so the spoke angle falls within a pretty narrow range no matter what. Heavier spoke wheels need to have the spokes "aim" at the corresponding hole in the hub. The rims are made "blank' with no holes, and they get drilled in the right spot in that little dimple to get the aim right. It is REALLY hard to tell if the angle is close enough without having all the parts in hand to see how things line up. It is possible to re-machine the rim, but I do not recommend it. The problem is that the hole is actually slightly not in the right place in that little dimple, so to get the landing for the head of the nipple to be aimed correctly, you have to machine material from only one side, making the rim very much thinner there. The hole itself is not really the issue, but the cone shaped counter bore that the nipple rests in. Take your wheel apart, look at the tire side where the spokes are held, and you will see that the nipples were only resting on one side of each landing.
I have machined rims to fix this problem, by taking one spoke out at a time, and cutting a new seat for the nipple. I made a jig that pilots a cutter for the nipple. the jig fits through the existing hole in the rim and locates in the hub's corresponding hole and guides the cutter. it is a pain, but takes less time than you might think. In practice, the cutter of course starts cutting only the "high" side, and I just manually stop cutting when it just starts to cut the opposite side. This of course makes one side of the "hole" a LOT thinner than you would like, which is why I don't recommend doing this unless the rim is pretty beefy, (thick). I have never had a problem, but I consider this risky at best. The alternative would be to slot the hole to bring the nipple around to the proper spot in the dimple, but I think this would be a lot worse. In any event, the best plan is to get a rim drilled for the hub you have. All pro wheel services will require you to give the hub spoke diameter in order to supply a proper rim. They will drill for that, not hand over a "front" rim they have on the shelf.
Of course, this is NOT your shaking problem. Balance or true (as already noted) is. Could also be a tire issue. Either the tire itself, or it not being properly seated in one spot. If you can rule this out, once you get the correct match rim for your hub, you should be able to do the rest of the work yourself. I really hate balancing weights on spoke wheels, so I always run the bike first to see if the wheels actually NEED to be balanced. Most of the time it is fine with no balancing, but I take my wheels to a friends dealership if they do. You have a pretty stout tire there, so maybe that's it, but personally, I have NEVER had a balance issue that was all that alarming. True is another matter. As others have noted, lacing is easy (mostly), and I think trueing is not so daunting as its reputation. I think anyone can do it if they have patience. Some rims are a lot not round, and are really hard to persuade, but mostly not. I still use a wood stand I built when I was a teenager. It is crap, but works fine. and I just use a pointer that clamps down near the tire side of the rim. I true to where the tire seats, and sometimes file the area where the rim is welded together to "straighten" it up a but if the factory grind is sloppy. Ther is a lot of advice on the web for truing wheels, but the bottom line is, go really, REALLY slow, make it round first, then tweak it flat. If you have stainless spokes USE ANTI SEIZE!!!!!!
hope something here is of use. Good Luck!