Make dnsmasq not altering resolv.conf

You don't need to list any nameserver other than 127.0.0.1 in /etc/resolv.conf. What you need to inform dnsmasq of the upstream DNS server, and it will relay and cache requests to the ISP's server.

If your ISP's DNS providers don't change (they rarely do), you can declare them in the Dnsmasq configuration file (/etc/dnsmasq.conf), with lines like server=203.0.113.1. If your ppp or dhcp daemon drops the addresses of your ISP's providers in a file, say /etc/ppp/resolv.conf, then reference that file in dnsmasq.conf: resolv-file=/etc/ppp/resolv.conf.

You'll find instructions for most common setups in the Dnsmasq setup documentation, and the complete list of options in the example configuration file.

If you're running Debian, Ubuntu or some other distribution with a resolvconf package, install it. Resolvconf automatically manages adding and removing entries from the DNS configuration when you connect or disconnect to a network.

On machine B, if /etc/NetworkManager/NetworkManager.conf contains dns=dnsmasq then resolv.conf should contain only one "nameserver" line, namely nameserver 127.0.1.1. 127.0.1.1 is the address where the NetworkManager-controlled local forwarding nameserver listens. NetworkManager gives that nameserver forwarding addresses to use.

Try running sudo dpkg-reconfigure resolvconf on machine B. This will restore the needed symbolic link from /etc/resolv.conf to ../run/resolvconf/resolv.conf.

Are you running a third-party VPN client? Such clients are known to clobber /etc/resolv.conf and not to restore it when they exit. You may have to do sudo dpkg-reconfigure resolvconf every time you stop such a client.

Another thing to try is: comment out dns=dnsmasq in /etc/NetworkManager/NetworkManager.conf and then reboot. This disables the NetworkManager-controlled local forwarding nameserver which has some known issues.