BS”D
TMB is 100% correct. The Husband’s parents go before the wife Halachicly (let us not sugar coat anything).
However, there are shibudim that a husband has to his spouse, that a parent does not have the right to interfere with (since that would be against the Torah, which then Kibbud Av V’em would not apply).
It is no coincidence that the prototypical case is “who goes first” for a glass of water. There are no shibuddim involved. If it was “who gets the water”, the wife would get it since he is Meshubad to feed her.
Besides, as Wolf points out, if a parent does interfere, the spouses will work on avoiding the conflict (or get a Rov to give them a Heter to completely avoid their parents for “Shalom Bayis”, which I heard has been done), including not picking up the phone & not visiting (both of which are not being “Over” Kibbud (IMHO)).