I bought the car a few weeks ago with the shaking it has thinking it would be a quick fix with some new lower control arms. I installed them and nothing changed. I will also note that the previous owner installed new engine mounts, transmission mount, wheel bearings and stut mounts. The wheels were also balanced.

I am planning on changing the front axle because that’s the only other thing that I think it could be.

the shaking is felt in the steering wheel and on the floorboard from what seems to be both front wheels. It doesn’t shake at speeds below 30 and gets worse at higher speeds and braking.

Any help would be greatly appreciated

 

Steering wheel shaking when accelerating - is usually caused by a worn cv joint. Usually in the right axle first, it takes most of the load/wear.

Shaking at speeds (not accelerating or decelerating) is something with the wheels/tires - out of balance, out of round, bent, aftermarket or non-hubcentric wheels installed, (xc90 wheels on a xc70 is an example).
Badly out of round tires due to tread separation vibration is felt beginning at very low speeds.

Shaking when braking is caused by the brake rotors. Warped, hot spots, pad material transfer, rust damage, etc.

 

so the car doesn’t shake at all when accelerating, it actually is quite smooth when accelerating.

the tires are brand new and we’re balanced before I purchased.

there is no shake when braking if it is under 30mph, I had brake warp before and this doesn’t feel the same.

 

Then don't change any axles because that won't solve any problems.

If your only complaint is shaking at speed and the original wheels are still on the car - then there is a bent wheel/s, out of round tire, or simply out of balance. (wheels weights fall off all the time, and "tire technicians" are really not at the top of the totem pole. Sorry, I owned a tire store and employed many fine individuals.)

If it shakes when braking - that's fixed with new/possibly resurfaced rotors. Most rotors don't get hot enough to actually warp. The shaking is caused by un even pad transfer that can cause "hot spots". (areas on a disc where the coefficient of friction is different)

 

the balancing happened last month and they are oem rims and brand new tires, if the rim was bent I would feel it at speeds under 30 mph and also during accelerating. I’m sorry but I don’t think that’s the issue.

I would also like to note that the previous owner took it to a shop so the shaking would be fixed and in doing that they balanced the rims and tires. I only bring that up because if that was the problem it would have went away when they did all of these repairs to fix the issue.

 

Sorry, but I disagree - personally I could not figure out why my 2002 xc70 would not drive smoothly at 80 mph. (I owned Volvo shop (38 years) and an expensive tire machine, a hunter wheel balancer and alignment rack - during that time) One of my wheels had a small hop in it. So I bought a used (round) wheel and - no more vibration at speed. That slightly bent wheel is now a full sized spare in that car I gave to my son.

Vibration at speed is caused by the wheels/tires. - and nothing else.