Can someone on the same wifi see your history?

The answer to your question - Can someone on the same WIFI see your history 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 specialized 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.