acess to computer by two remote possibilities

Hello!

I have a server which actually hangs on an cabled Internet connection with a router between and I have a Huawei GSM modem. I do not have always physical access to it and it is used solely over RDP connection.

I have the problem, that sometimes the internet signal over the wired connection ceases to work, i.e. no site is reachable because the provider do not deliver the signal properly, but the system does not recognize it and I would like to remotely change the whole internet traffic to the GSM modem updating the IP over some dynamic IP service.

I was thinking about the following scenario:
- Having the two connections active, but primarily using faster and cheaper wired connection for RDP traffic.
- When the signal is lost, I remotely access the system by GSM modem and dynamic IP service and route all the RDP traffic over this connection
- When the wired signal is back (or after some time) I switch back to it, remotely.

Now my questions:
- How do I get the computer to hold two connections at the same time?
- Is it possible to access the computer by RDP via cable or GSM modem at the same time?
- Am I thinking to complicated and there is a easier way out?

I really searched a lot, but did not find a topic equal to my needs. If you have some ideas or links for further reading I would be very happy to hear them.

Please bear in mind, I am situated almost in the Brazilian jungle, so access to some fancy hardware is more than complicated for me.

Thanks for any ideas!

Somebody? Please?