It's all "different strokes for different folks". Not all cuckolds are the same any more than all bulls or all Wives. Everyone has their own particular needs and desires and as long as there is some common ground for all of them, they will find something that works.
The particulars of how their relationship works is between the Wife and her husband as is the relationship between the Wife and her lover.
The relationship between the Wife's lover and her cuckold should be decided on between the Wife and her lover based on the needs and desires of all three participants and then implemented according to what will work best for all concerned.
In my case, I serve my Wife and her pleasure. She accommodates my needs and entertains my desires at her pleasure and in whatever manner she decides pleases her the most, not that which would necessarily be my choice.
My Wife understands my need to occasionally experience deep sexual humiliation. Therefore, when the mood strikes her, she will entertain herself by placing me in a situation designed to create the type of humiliation that I crave, but never in a harmful way nor does she ever include a third (or more) party without making sure that they are willing and comfortable with what she is planning as well as getting their input for alternate ideas.
That said, if my Wife wished to include such a humiliation scene into a date with a lover, she would negotiate what role and what activities the lover would be comfortable with. That would determine the extent of what my involvement with their "date" would be. It might not be anything more than serving refreshments when called on to do so.
Keeping in mind that just having a Wife that enjoys sex with others can be a humiliation in and of itself, it can easily be compounded by having the cuckold prepare his Wife for her date by helping her bathe and dress, shaving her cunt if she shaves it, etc. knowing that he is preparing her for another man's pleasure.
Have him chauffeur his Wife to where she is meeting her lover.
If the lover is to be entertained at their home, have the cuckold greet him at the door and then lead him to the bedroom where the Wife is lounging on their bed, take his coat, offer and serve refreshments and then retire to another room until called. Adding the cuckold's presence in a different room so that he is faced with his Wife's infidelity even though he can't see it is extremely strong.
Have him serve refreshments and act as a butler on call.
Ramp that up by making him remain in the room so he can witness his Wife's infidelity.
Have him participate by undressing his Wife for her lover.
Have him eat his Wife's pussy or ass to get her wet or put lube on her to ready her for her lover's cock.
Have him hold her lover's cock and position it for entry into his Wife's cunt or ass.
Have him stand by to reinsert the lover's cock should it "accidentally" slip out.
Include him by having him perform oral on his Wife while her lover is fucking her.
Have him lick his Wife clean in front of her lover after he has ejaculated inside her.
Have him clean the lover using warm damp washcloth and towel.
Have him lick the lover's cock clean as well as his Wife's cunt.
Have him "fluff" the lover to ready him for another round of fucking.
ETC ....
Obviously the list could go on to ever increasingly humiliating tasks, BUT the point is that only those things that are comfortable for the bull to do and which are negotiated by the he and the Wife before hand would be utilized.