I don’t think mums favour daughters, they just step back when their son gets a partner/wife. Mine all live at home still but I have seen this with many friends.
The rule of thumb is that the daughter tends to take on the ‘rules’ of the household pretty much aligned with the mums rules for her household. Certainly not always but probably in the majority of cases I have observed. So a mum is more comfortable in a daughters house as there is a common understanding for the majority of stuff. It’s also easier if there is a misunderstanding or discrepancy to thrash it out with your blood child.
Contrast that to a sons household where the DIL has unknown rules and expectations. You see it all the time on mumsnet - she comes here and just waltzes into my kitchen and puts the kettle on like she owns the place/she sits there and expects me to get her a cup of tea and wait on her (either way mumsnet says, what a bitch, go NC). MIL’s just can’t win. Given every social interaction there is now a fraught guessing game of what rules the DIL seems to have for her household/the grandchildren, mothers tend to be more comfortable staying at their daughters as a general rule. Also, if there is some breach of ‘the rules’, rarely does a mother get to sort it out with her son as the DIL tends to insert herself front and centre.
Same with gifts, some mothers I know are that scared that ‘yet again’ they will buy the wrong gift as the DIL seems to have rules that it must be made from something organically harvested from virgin rainforest by a troop of magical pixies and washed in unicorn tears before being wrapped in a banana leaf, no bow. Generally the son couldn’t give a rats what the gift is but the DIL seems to have ‘rules’ and will be straight into mumsnet to bitch about it the minute his mum has stepped out the door.
Mums love their sons as much as their daughters, it just gets complicated when the son gets a partner.