I spend quite a lot of time in a nearby coffee shop, and as a result also use their internet a lot. The problem is that the DNS servers their network offers by default are terribly slow (~1s per request), and since they use a (poorly implemented) captive portal to get customers to login, using a public DNS server like 1.1.1.1 or 8.8.8.8 makes it impossible to login.
To make matters worse, the DNS server used by default seems to change every few days, so in order to use their network I have to set my DNS settings to 'Obtain DNS server address automatically', login, and then change them to something more usable.
So, how can I make this less miserable? Is there any way 'Obtain DNS server address automatically' can be used as a fallback to my preferred DNS server?