I house trained my puppy in week. 7 years later and she's never had an accident in the house.
What did I do? I treated the task like a full time job.
Puppy was crate trained into a crate not too big. This way she had her safe space where she was happy.
Nighttime: Every time she came out of her crate (overnight) she was picked up and carried to the garden. This didn't allow accidents en route. Any noise during the night from pup, I immediately shot up (no matter how tired, raining etc), quickly downstairs (no words to pup), carried pup to the garden and waited in silence. No other interaction just a calm good girl when toileted, nothing more and back into her crate until morning. Unless of course she barked again. Then it was up again. The investment was worth it.
Daytime: I turned into a hawk. Tied to me with an indoor training lead a puppy will ALWAYS give sign they need to go.
Daytime: After ever drink and every meal, straight out into the garden. No words, just wait and watch until the deed is done. Then crazy praise and a tiny treat STRAIGHT after.
Then moving forward, when she was toileting I add a word.... we used wee wee, or quickly, every time she went. Followed by the praise and infrequent treat reward.
She now goes on command.
A second dog especially a puppy, is a little like having a second child. Sounds like a great idea, but in reality is so much harder than you thought. You must have evaluated this before buying a new puppy. It's only fair to put the required work in, to give the pup the very best chance of having a loving secure home for life.