Players in LAN multiplayer can't use inputs

It seems like you’re not sending your movement commands to the server. Clients perform the said actions, but snap back after receiving corrections from the host. To confirm that it’s the case, you can type “p.NetShowCorrections 1” in the console, and perform some double jumps on a client.

There are several ways of implementing movement abilities, there’s a great overview here: Character Movement Component | Unreal Engine Documentation

For a start, I think you can take Approach 3 from the above article: trigger an ability locally, and tell the server to do the same using an RPC (or function replication). To make it in Blueprint, check out Part 5 of these tutorials: Blueprint Networking Tutorials - Unreal Engine

I hope this helps!