How do I fix my sister's wifi?

You can’t just fix speed, it depends on what internet package she is using. As for the IP just google change mac ip address and that should help.

Sounds like there is something wrong with the DHCP in the router. That’s the service that assigns IP addresses to WiFi devices that don’t have an IP pre-assigned. There should be a pool of IP addresses allotted to the WiFi machines. When you’re on the WiFi on the Macbook, the router should not forget that and give your IP to another device, it should give the other device a different IP address, usually the next higher number in the pool.
You might need a new router or an upgrade to its firmware.

As an alternative you could assign an IP address to your Macbook’s WiFi interface that is outside the DHCP range of IPs in the router.
If you still get kicked out because the router can handle only one device at a time, then you definitely should consider a new router.

Yeah, it’s a very old router and I can’t convince her to get a new one cause she says it works for her. I’ll try out changing the IP address on my Macbook myself. Do I just pick out a random IP number and hope it works? I’m assuming I should just add 1 or 2 at the end of the IP now.

The first thing I would do is check the router settings, because that’s where you can set a limit to the number of computers that can use the network at one time. You’d need to type the router’s address into your address bar, then enter her username and password. You need to be connected to the internet to do this, though not necessarily her network. If she’s this uninterested in helping you get onto her network, you might be out of luck getting that security info. A lot of people just forget this even exists once they set up their router.

Make sure NAT is enabled. That is what enables DHCP to do it’s stuff.

Find the manual for the router online at the manufacturer’s web site.
The default IP address of the router will be listed in there and it’s very common to leave it the way it came from the factory.
The typical default address for routers seem to be 192.168.0.1 or 2.
The manual would provide default administrator accountName and password, and it’s possible that router still has those (It’s highly recommended to change those).
If the password has been changed and you, or she, don’t have the password, you probably won’t be able to see much on it, and you won’t be able to change or fix anything.

If you are willing to set it up from scratch, get the manual and read over the steps for setting it up a couple times, then find the little button that will restore factory default settings.
Get her permission to do that before starting.