Either use HDMI CEC (try to press the arrow buttons on the TV remote to see if it reacts) or create a hotspot with your phone, name the wifi network the same as your home network it was originally connected, same password (you can also try to to disable the password, I think it can automatically connect that way too) , reboot it to see if it automatically connects to wifi so you can either cast stuff via Chromecast from your phone or configure the Android TV remote app
I think the android remote app works with Bluetooth too, though it never worked on my TCL (no surprise here). Have you already tested it?
Other option/hope is having a new'ish tv with hdmi-cec controls and that you had hdmi-cec option enabled in mistick.
Connect temporary mouse trough usb, connect wifi, and then use Android tv remote, phone must be in the same network
https://play.google.com/store/apps/details?id=com.google.android.tv.remote
Is that an Android phone? Try the Android TV remote. https://play.google.com/store/apps/details?id=com.google.android.tv.remote&hl=en_US&gl=US
If the HDMI-CEC setting is on, you should be able to control it using the TV remote (if it's not an old TV)
Please try Zank remote for Android TV box with mouse functionality .
The time and effort spent on a holiday trying to solve such a problem will cost more than a new mi stick.... Not to mention the frustration for both you and your loved ones.
Is there nothing else you can do to take advantage of being away on holiday? Your TV will still be there when you get home.
android tv remote app works perfectly well with mi tv stick both devices have to be connected to same wi-fi.
Good luck.