A extender will work and in this case is going to be simpler than what is normally discussed here to solve your issue. You have more options when you have a wired ethernet port to work with.
I have done similar with a spirnt evo phone acting as a hotspot. The major problem with extenders is you now have 2 radio links to deal with. One between the extender and the hotspot and a second to your end devices. You still have all the same issue getting signal to your end devices. You now need to find 2 channels that do not interfere with each other as well as do not have too many other people using them. It is somewhat simpler to use 2 different SSID so you know which device your end PC are talking to.
It is just very tedious to set up and get working. It will be a just a little slower since you have 2 radio hops but compared to cell broadband you should not see it.
The key reason this device (like most cell phones) has low power is that it is portable. The internal parts tend to give up coverage to improve on battery life. I would see if the vendor has a normal full size wireless router they can offer. They also make USB stick cell modems that you can attach to a third party router, the vendor should be able to recommend one that is compatible with their modem.
I just signed up with Clear and received their Spot Voyager. The speeds are decent for what I need right now. The only problem is that the range is really only strong enough for one room. I am trying to increase the range so that I can get internet access on two floors. I am not sure what I should do since the Voyager has no ethernet ports. Would a wireless extender/repeater work with the Clear Spot Voyager? If not, do I have any other options?