it's my understanding that the qadha namaaz of a mother who has passed away and had no son can be read by either her daughter or son in law.
what would the niyyat be? does one have to mention that it's for their mother and take her name for each namaaz ?

It is not wajib on daughter and son in law to pray but yes they can pray and they can hire to pray on behalf of her
Niyat will be like I’m praying two Rakat fajr qadha of … qurbatan ilallah