Couple thoughts regarding this...(it's long because some background explanation is needed first
Once they're spayed, they'll need some down-time to recuperate. That'll mean limiting their space for that. Once they are ready to have more space, it's best to increase that space in small increments. If rabbits are given too much space to roam all at one time, they are more likely to 'forget' where their litter box is and have potty accidents.
Any potty accidents are difficult to undo because they tend to go where they've gone before. Far easier it is to keep them going in their litter box than to try to stop them from repeating a potty accident.
As for the idea of their regular living space and a separate roaming space.... having those 2 areas separated is not at all ideal. Wherever a bunny is going to be permitted to roam, he should always have easy access back to his "home." This has to do with more than just the litter box. Whatever their usual "home" space/cage is, that is their "safe zone" (in their mind). That means that blocking them from being able to get back there at will is not good. For their own comfort and feeling of "safety" they should be able to return to their own space whenever they feel so inclined.
With that in mind, then, it may be best to have their home base be set up in the living room (if that is going to be their roaming space). Having a separate bunny room may sound ideal, but oftentimes these "bunny rooms" end up keeping the rabbits from having much interaction with the family. They are out of sight of people and people are out of their sight for all the hours the rabbits are confined to their own room. Their interaction is limited to when they are allowed out elsewhere.
If they are housed in the main living area, on the other hand, they are seeing people almost all the time -- even if the rabbits are not actively roaming about. This proximity/sight of humans helps them to form a bond with them even when not directly interacting. They are still becoming accustomed to the presence of (bonding, in fact with) the people.
So, all that lengthy explanation to get to the issue of extra litter boxes. The rabbits should always have easy access back to the litter box they are used to using. Litter boxes are usually associated with a location. If a litter box is always in a particular corner of a room, moving it somewhere else may cause them to still potty in the location/corner the box
used to be. It's about location. One could add an extra box somewhere else and see if they decide to potty there
in addition to their regular box.
If they are moved to a totally different room for roaming that has no access back to their home/usual room, then they will need to be potty trained again for that new roaming space. If the space is a decent-sized room, then this process will have to take some time because they should not have access to the entire room to begin with (otherwise they are likely to have a potty accident which we know is hard to un-teach). For such a new room, they'd have to be confined to a small section of the room to begin with. That small section will have its own litter box. They'll have to get perfect with using that litter box in that confined space before having that space expanded. Over time, the space can be expanded, provided they consistently return to that potty box as needed. So it will be a process that could take a number of weeks before they can roam the entire room and still potty in the 'new' litter box. (placing 'used' litter in the box can help)
