Welcome to the forum
I’m afraid the advice you have been given is completely incorrect and is likely to cause huge issues. Neutral territory is completely essential for every bonding.
Please immediately end the bonding and separate them if they are fighting or if acceptance isn’t occurring.
Adult piggies ideally need to live in side by side cages for a week or so to get to know each other between the bars before you attempt to bond them. There is no point in trying to bond new, scared piggies or piggies who until the point of bonding were unaware of the presence of the others. Allowing them a week or so side by side allows them to settle in and get to know each other a bit before you put them on neutral territory.
You absolutely must do a bonding properly on neutral territory.
No hides should ever be used in a bonding pen because they create territories, and the whole point of a bonding pen being neutral is that no territories can or should form.
You cannot just put new piggies into the cage/territory belonging to others (even if you have cleaned it). It will be seen as an invasion and will cause a fight and failed bonding. Your dominant sow is defending her territory.
An 11sq ft cage is not big enough to have four piggies in any event so it was not a good idea to try to bond them somewhere without enough room. If it was an experienced rescue that you got the piggies from then they should know that 11sq ft is not big enough and reputable rescues would not allow piggies to be rehomed where there is lack of space and while also providing poor bonding advice.
I would also be questioning their quarantine status. Piggies from anywhere other than a reputable rescue should be quarantined for two weeks in a separate room from your other piggies before having any contact with your piggies.
If they are able to stay together through this (Ie if the bonding has not failed) then when you change the cage to a bigger cage, it will cause them to have to reestablish their bonding all over again so further rounds of dominance for two weeks (bonding in the first place takes a total of two weeks following a successful neutral territory introduction in any event). Therefore they should go into the right size cage straight away (once moved from the neutral pen to their permanent cage) to avoid new rounds.
Light/dark does not make a difference.
You are also attempting a combination of piggies which could have issues.
Joining two already bonded adult pairs means there is already a dominant sow in each pairing. Due to the fact a herd will not work for two dominant sows, it means that when merging, one of the dominant sows has to be prepared to step down and lose her position. That is usually not something they are prepared to do (particularly once they are older*) so you need to be prepared that this bonding may not be successful, particularly if you don’t do the bonding properly.
*we would have recommended that piggies younger than your original 1 year old pair were introduced ie babies. That way they would have been more likely to submit to your 1 year old dominant sow and the bonding go well whereas a 2 year old dominant is not likely to submit to a piggy younger than her. You would never be advised by us to try a bonding which disrupts the existing hierarchy like adding a 2 year old pair would do.
The older sows get they tend to get less willing to accept change and the 2 year olds may be more tame but being tame to humans does not make a difference to their nature and social structures when it comes to other piggies.
If a fight has occurred or the bonding has not been successful ie they have not accepted each other, then I'm afraid you cannot try to put them together again. They don’t change their minds after an unsuccessful introduction or fight so they would need to live in two separate cages permanently and have no physical interaction with each other for the rest of their lives.
I’ve added two guides below which explain more
Adding More Guinea Pigs Or Merging Pairs – What Works And What Not?
Bonding and Interaction: Illustrated Bonding Dynamics and Behaviours
