You may do well to obtain an external antenna, either omni-directional or directional antenna (if you know for certain where your nearest cell antenna is, and can point it there with a clear line of sight). This antenna would need to be mounted outside your home or office.

That tiny connector there should be called an “SMA” connector, and the specific antenna you need will depend on which cellular technology you are on, 4G, LTE, and so on.

Before buying anything to supplement your hotspot, it may be worth checking to see if your issues are even caused by poor signal strength. Depending on the cause, buying better antennae or a signal booster relay may not provide any tangible benefit. As you say you live in a rural area, your issues may be unsolvable by different hardware as your device may be throttled by your carrier instead.

Out of curiosity, who do you use to provide internet?

I'm not too familiar with wifi routers, but I've been using my phone exclusively for internet for the past 2 years.

It's possible you're just with a company that doesn't provide good service. I use Visible for $25/month and it gives me access to Verizon's network with unlimited data and no throttling, provided there's no congestion (which there pretty much never is.)

I don't have anything to add technically and there may still be a technical solution to the issue, but on first read I thought the increased humidity could be affecting the signal, but it might be that when it's rainy more people are inside and streaming and contributing to the total load of the network.

Considering looking up if any WISPs service your area. It's land-based wireless internet not satellite, and with a good service provider you could be able to get the same kind of speeds you would get in a well-served city. The only downside is you would need a clear LOS to a service tower, so if your home is surrounded by really tall trees, you might not be able to get it without installing a pole.

To start with what 4g modem did you get and what country are you in?

Those are important because not all modems have the same RF ports some are N type, some are sma, some are sma-rp so we need to know.