if i understand you correctly then you most likely you want to set up a vpn (virtual private network) connection to you work network - that way you can route all traffic from that domain through the vpn and the rest through the other connection.
But setting up a vpn requires your work to have the abilities and hardware to do so, and it needs to be configured correctly.
When all set up you will have one connection to work and another to the internet. The work connection will be secure as long as the vpn server is set up to use a secure protocol. These two connections will quite hapily run side by side.