From your description it sound s like your phone is connecting to BTWIFI and not your home network when at home. You should be able to set your phone to connect to your home network at home and not BTWIFI
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Sounds like poor mobile coverage inside your house tbh. Might be worth seeing if your handset has wifi calling, as that will get you connected to the network via wifi. Helps me out as i don't get signal in my house either.