Check this Icom RoIP software out. It may be what you are looking for.
https://quality2wayradios.com/store/icom-roip-software/icom-rc-fs10
While the RC-FS10 Communicator package is a fine application, it will not do what you want. It is strictly a PC RoIP interface.
The F5061 has no IP capabilities directly; to use the FS10 you have to have a VE-PG3 to interface with the F5061, and even then the radio will only send audio from the channel it is on (or in the scan list) and TX as programmed - no channel changes. It is possible to set talkback for TX on the last RX channel for "X" seconds, but that gets a bit dicey.
If by remote control you mean hard channel changes, the F5061 DB-25 allows you to input a binary code via a five-wire input to change channels. An external box like a CPI TTP216 will take EIA audio control tones and translate that to the combination of +/- on the channel leads to select a channel. The radio looks at them for a binary value set up in the cloning software to indicate the active channel. That is normal for dispatch console integration. The TTP216 is connected to translate the audio for 600 ohm -10db audio I/O over two- or four-wire, and also uses the EIA control tones to put the radio into TX or monitor mode.
Either way you are starting at well over $1K to move forward. If you don't need to TX a good scanner with a serial connection is probably a better solution.
I have no recommendation, but any IP enabled device with at least five outputs that can go 5VDC+ or 0V on demand will trigger the channel change matrix in the radio. You're on your own there, and will need to work out the pull-up/pull-down resistors to hold the binary inputs in the right state.
If you have a PC at the radio, you can leave the programming adapter plugged in and write a new file to the radio for each change you want to make. Unlike earlier radios the F5061 will fully reboot after a clone write, and come up in whatever state the icf file says to start in.
Sorry to say that this is not a simple project.