If the non-custodial parent lives in a room in a shared house it is arguably reasonable for the child to visit there.
The term "co-habitation" does not always mean just "living together as sexual or romantic partners", and the way in which this quoted section of the agreement (if it is part of an actual agreement applicable to the specific parent) is worded makes it possible that the agreement is intended to cover more than that.
However, the most usual meaning of cohabitation is "living together in a way similar to marriage" and it generally implies both a sexual and a financial relationship (sharing expenses as a typical married couple does). Statutory definitions, where they exist, vary by state.
This is shown by several available definitions:
- US Legal -- Cohabitation is generally defined as two people living together as if a married couple. State laws vary in defining cohabitation.
- The Free Dictionary:Cohabit -- persons living together as husband and wife, whether or not legally married.
- The Free Dictionary:Cohabitation -- A living arrangement in which an unmarried couple lives together in a long-term relationship that resembles a marriage.
- LII -- Cohabitation is used primarily to denote the arrangement between two individuals who live together, either as spouses or unmarried partners.
- Reuters Practical law -- A living arrangement whereby a couple who is not married or a couple who is in a civil partnership live together in the same household.
- Wikipedia -- Cohabitation is an arrangement where two people are not married but live together. They are often involved in a romantic or sexually intimate relationship on a long-term or permanent basis.
- Lexis PSL -- [too long to quote here]
It might be argued that if the parent has a separate room, under a rental agreement, a person not sharing that room is not cohabiting with the parent. It certainly can be argued, based on the definitions above, that where there is no financial sharing, and no sexual or romantic relationship, there is no cohabitation.
One very relevant question is the purpose of the provision. One possible purpose is to prevent access to the child by adults not known to the custodial parent, in fear of abuse, neglect, or other improper actions. If that is the issue, it should be possible for the custodial parent to approve the housemate as a proper person to be present during a visitation.
Another possible purpose is to avoid exposing the child to an out-of-marriage sexual relationship as a "bad example". This is sometimes called a "morals clause", and was once common. This is largely obsolete, and if this is the reason, the agreement should probably be changed, but it in any case should not apply in the situation described by the question.
It might be a good idea to reach out to the custodial parent, or that parent's lawyer, and ask why the provision is in the agreement, and whether it is intended to apply in this situation. That will allow proceeding on a more informed basis.