Can someone see my internet history if I use their wifi?

The answer to - Can someone see my internet history if I use their wifi is yes, they will be able to see what you are doing. Firstly, if the website you use does not use HTTPS, they will additionally be able to see any data you are sending, and tamper with it at will. Secondly, they will be able to see the domain you are visiting regardless of encryption status, which itself would likely be pretty incriminating. One solution would be to use a VPN, but be aware that many commercial VPNs can be defeated by a sufficiently tech-savvy attacker. This is because VPNs are designed only to be shared by people who mutually trust each other. Against most people, they are sufficient.

Another thing to be aware of is traffic analysis against videos. This is an issue because video formats are compressed. This causes the raw upload rate to differ over time based on how effectively the given section of video can be compressed. This variable upload rate can be used to identify the fact that a video is being uploaded even if encryption is being used, though in most circumstances it cannot determine what the video is of. There is no effective way to prevent this while doing live video broadcasts if you are on their Wi-Fi. Anyone who looks at the logs will be able to see you uploading a constant variable-rate stream of data. This just screams "streaming live video". Doing this for 6 to 9 hours a day (as you mentioned you do in a comment) may be suspicious to anyone looking at your traffic flow if you don't have another reasonable explanation (e.g. remote meetings).

There is a simple solution, however: don't use their internet! This is easier than it sounds. You can buy a USB 3G/4G/5G dongle which will provide you with high-speed mobile internet (although not enough for HD video). You would likely want to purchase an unlimited data plan if you are uploading a lot. The only way to view this traffic would be to use specialised hardware. This is not likely unless your family is really interested in what you are doing. Chances are, they will not even know you are using a mobile dongle unless you tell them or they actually see it (and know what it is).

Note that not all areas have great bandwidth, and whether or not the upload bandwidth is sufficient depends on how high your video quality needs to be. I've been able to stream video over 4G and was satisfied with the results, but your mileage may vary. Test it out before you rely on it.

Although the above should be sufficient for a general answer, you need to formulate a threat model, determining who your adversaries are, what positions they are in, what resources they have, what they are after, and what your assets are. Ask yourself a few questions. You must:

Determine the level of sophistication of your adversaries. Do they merely know the basics of networking? Does their profession involve network analysis? Are they PhD researchers who put out their own novel research related to networking? "Tech-savvy" encompasses many things.

Determine your adversaries' capabilities. Are they only able to access their own router logs? Do they have access to your computer, potentially allowing them to tamper with it? Is there a risk that they will walk in on you doing your cam shows? Might they overhear you outside the door?

Specify your assets. In other words, are you trying to hide the contents of the videos, their destination website, or the fact that you are uploading videos at all? Is it specifically the fact that you are a cam model that you are trying to hide, or exactly what requests you get from clients?

Quantify the threat. Do they not care at all to find out what you do, making accidental exposure the biggest risk? Are they merely curious about what you are doing? Are they dead-set on finding out?

Analyse the risks. Would knowledge of the fact that you are a cam model simply be embarrassing? Would it risk you being disowned by your family? Would your very life be at risk?

Here is a hypothetical example of what a basic threat model might look like:

My adversary is my tech-savvy uncle.

He is a snoop and doesn't like the idea that anyone is doing something in secret.

He does incident response for a large ISP, so he knows the tricks of the trade.

He can only log network activity, not install cameras or tamper with my computer.

If he finds out what I'm doing, I will be pressured to stop and may lose my source of income.

A threat model will allow you to determine the best way to protect your assets.