All of these are sound advice. I am going to let this idea fly and an option- yes, this is unsolicited advice, but I will give you my sincere professional “inferior design” advise (as Lil’ Mikey would say). The obvious is the hardest challenge you have is to match existing- difficult task because it is a stain. What happens with stain finishes is they develop a patina over time. So you have this difficulty of “marrying old and new”. It will be a challenge not just finding the base stain, but it might requiring “tinting” or using a “toner” to match it as close as possible. You also need to know what type of maple species that is existing, because naturally they have different shades in its natural state. You don’t want the existing when you stain be a shade or tint different than the new or vice versa. So these are the given challenges.
This is what I would personally do with this project. When clients wants something functional to be retrofitted into an existing- it will fit the requirement of function, but it doesn’t always mean it would look aesthetically correct and balance. In a practical view point- the drawers should be on the right. This way, you can still open the drawers on the right hand side and pickup what you need there and still be able to shuffle left and have space clearance (say for a woman to do their hair or make up)- if you did it the way your MIL proposes then you have that awkwardness and not have a more workable clearance. That is in a design point perspective. My solution is fairly simple and it means keeping what the existing conditions intact. That means the door stays. What changed is the right hand door side, you create a drawer box compartment that slides into the cavity- guess what if you want more plumbing clearance, the drawer boxes can easily just pop off the glides. You end up with an interior drawers inside and allow for filler for drawer clearance and for access to plumbing shut off valve. You can use birch as it is very similar to maple. Staining it would be easier because you can get close to the base stain and if it is a shade or tint off, it will look alright as it will be concealed by a door.