I might be having the same issue! It never occurred to me to try disabling BT on the slave, but after trying it mouse input from the main does seem to behave a LOT better when it's disabled. Luckily I generally don't need to use BT at the same time as Input Director so it isn't a huge deal for me.
What make and model device is your slave device? Mine is a Dell Latitude 5430. Main is a desktop. Both are connected to the same LAN via Gb ethernet.
Do you see "Network errors" reported in Input Director after a bout of the mouse getting wonky/sluggish? The slave device reports errors (wish I knew exactly what those "errors" consisted of...), while the main reports zero.
Do you have a "Preferred Network Interface" configured on the slave? I do (to keep it away from the VPN client) but it doesn't seem to make any difference in terms of this issue.