Her Gorgeousness over in Frankfurt has the same problem with DSL broadband in heavy rain.
"Nein", said T-Online, "It must be your modem"
"Modem is fine - and how does it know when it's raining?"
"Zis cannot be so."
"It is. Maybe you could check your cables?"
"Zis ist not ze normal procedure"
A few days later, a gang of telecom engineers were observed opening man hole covers, tutting and shaking heads. Funny old thing, the next time it rained the problem had gone away.....
Persist with the 'external' line provider and don't be fobbed off by some idiot claiming your 'settings' are incorrect!