If you are looking for an alternative to TeamViewer and AnyDesk, you might want to take a look at Rustdesk.
Open source, cross platform and you can even set up your own rendezvous/relay server if you want to make sure you control everything.
There are no restrictions on the software. Use it on as many computers you want, both personal and business.
I have tried it out for a little while as I am the go-to IT person in my (rather large) family. It definitely works for this purpose 