BM doesn’t fight intelligently. She’s never needed to be intelligent because she was born supernaturally strong.
Shanks identified Kid as a threat and ended him before he could cause any real damage. Absolutely nothing suggests BM is far weaker than Shanks. She has ACoC and split the sky with Kaido, she is a yonko, and her bounty is actually higher than Shanks’s.
The difference between the two was Shanks was smarter. He didn’t underestimate Kid. BM underestimated both of them. She literally turned her back on them to go fly to Kaido. When Kid pulled up with DP, BM was shocked he could still fight and had something up his sleeve.
Again, the underestimation/character-was-just-stupid argument is just headcanon that tries to explain Oda's lazy writing. That still doesn't explain why she wouldn't just use one of her essential abilities. Why was she using all of her higher power DF tools if she was just underestimating them?
You're right, they got their stamina back after being on the brink of death, for no reason. I'm not surprised BM was shocked, she may have realized then that she was battling extreme plot armor. That particular moment when Law was just kneeling in place, completely defenseless, on her stomach was after they got back up for the millionth time by the way. I guess she was still just underestimating them, fuck it don't use ACoC punches.
Also, "not fighting intelligently"? Where are you getting that from exactly? You're just assuming she never does/has. Again, you're just writing the story for Oda.
All that that Shanks scene showed is that the fight with Big Mom was completely nonsensical. Midd should have died ages ago.