i hope they get along! When I had a westie i made the mistake of petting my neighbor's dog in front of him and he headbutted her away because he did not want to share me with other dogs. They can be very possessive of their owners.
Westies have a fine attitude to them. My late westie, Hamish, would go outside and see rain then just stop with no intent to cooperate. He sadly developed a tumour. One of our last few walks he was completely happy walking in the wind and rain in his jacket for an hour and I ended up cutting the walk short because it was too cold for me in a big jacket. Cherish this dog.
I had a Westie for 15 years. He could not stand walking in the rain, and would do everything possible to avoid it. He would also behave like your dog when he was very tired and he was on too long of a walk and didn't have enough water, or if it was too hot and humid. Your dog is also probably a little more tired because of all the puppy energy. It's best to walk him after he has eaten; otherwise, he may not have enough energy for the length of walk you have him on. When they lie down and no longer want to walk, it's best not to force them to go on and just pick them up and carry them home.
This was such a sweet video of your older Westie with the new female Westie puppy. I too will be getting a new Female Westie puppy on 24 Sept 2022, this Saturday. She will be 8 wks. old and we are planning to name her Ellie. My husband wants to call her Ellie Smelly. We don't have our older Westie, Lilly, she died on Thanksgiving last year at 17.5 years old. I hope to get another female to keep Ellie company next year when Ellie is older. Then she can be the older sister.