Can a father have another woman sleep over (not remarried yet) when it is his turn with the children?

Yes.

Do you have other concerns with this woman?

Yes I do. And I don't think that it is right to confuse the children at this point.

You are going to have to give more information. Is it illegal, no. Will it lose him custody, doubtful.

What are your true concerns with him having his girlfriend spend the night when your children visit?

Can a father have another woman sleep over (not remarried yet) when it is his turn with the children?

Yes. Is there something wrong with consenting adults having sex in private when they are not married to each other? It's not only not illegal, it's constitutionally protected behavior in the US.(Lawrence v. Texas (2003) 539 U.S. 558)

It all depends on the details.. example.. do your children know this lady?
Is she apart of your life?
Will the kids be freaked out if they see her in the morning?
There's no problem having this lady stay over with you,but I would reconsider if its just a fly by night thing and the kids are around,what if one of the kids get up during the night,or is sick? I'm just trying to play the possibilies.

IF it is in the court order that the parent can not have their girlfriend or boyfriend staying there then it is not okay. I have seen Judges put the stipulation in the order because they felt it was in the best interest of the child that it not happen.
If you can prove she is detrimental to your kids and the Judge feels it is warranted then you might be able to get it in your custody orders.
The decision isn't yours at all. All you can do is voice your concerns and if it is really bad take it to court with documented proof.

Can you explain more, but normally this is no legal issue at all