No. Read on only if you're curious.
Not unless you own the network connection that the Roku is on. If the residents share a network connection provided by the nursing home, they won't grant you a VPN connection to it even if the server exists. If you paid an ISP to install a connection and pay monthly for it just for your grandmother's use, then you'd need to purchase a router and set it up, including the VPN server, and maybe set up DDNS, providing the nursing home grants you access to install this stuff, and if you need further explanation, you'll need to pay someone to install and set it up for you. Not trivial, and probably not possible at all.
P.S.: I'm only saying it might work with the VPN. I haven't tried it myself yet.
P.P.S.: Didn't find the Roku, didn't work for me on first attempt.
P.P.P.S.: Doesn't work with OpenVPN. It appears that the Roku won't allow the connection from the Roku app unless it originates from the same subnet.
