OBS is only set up to stream to one place at a time. This is what services like restream.io are designed to handle.
It is possible to run one instance of OBS with an NDI output, and then run 2 more instances in portable mode that just have the NDI source, each broadcasting to their respective destination (twitch for one, youtube for the other). This would honestly be the simplest way to handle things locally if you don't want to use restream.io or another external service.
Keep in mind though, each instance of OBS will require all the resources necessary for scene rendering and encoding, so this is not something that is really within the normal use case for even higher end systems.
tl;dr use restream.io for the easiest experience. If you need higher quality/lower latency, then there are ways to do it.