No the visitation is up to both parents. I am currently in court with my ex over custody and if he is to win then all he put in for visitation was as agreed the judge actually made him come up with specifics cause if we do not agree if he wins then we will be back in court... I know what you mean as my ex had nothing to do with my daughter for 6 years and all of a sudden he has settled and about to marry and they want to play happy families... but my daughter loves him and looks at him in totally different eyes to mine.. I cant stand him but i Tolerate him for my daughters sake.. She needs to know her dad. i would ask that he comes up with appropriate bedding for the child but it really isn't that big of deal if she is only staying 1 or 2 nights but any longer and bedding needs to be sorted.. even if its on a sofa.. Once they are older they really do start to see the whole picture.. My daughter is 8 and really knows that her father gives her what she wants and she takes advantage of that... when she went to visit him for the school holidays for 2 whole weeks she did nothing but sit in the house and wait for him to come home he had no time for her she is quite happy with all the clothes and accessories but when it comes time to visit him she cries and carries on but i think its important that she experiences this as she is just not going to given things for nothing she has to realise that yes there is a give and take... but she is definately seeing the full picture.. and in time your daughter will also see for herself this way when she is a teenager she cannot blame you for not knowing her father she will have had the oppourtunity to know him and decide for herself..
EDIT: chase this child support.... It really works against him in the courts if he is not up to date. Oh and i would not let my child go to any house that i did not know the address of... So until you get the address then i would not be sending her.
Other than a screen shot of your history list showing those sites or printouts of the webpages, there is no certification that i am aware of in existence. In any event, I cant see how that would have any relevence in a legal action.
The only relevent evidence would be the police reports of domestic violence and medical evidence submitted by the plaintiff.
Evidence of your research into domestic violence would not benefit the actual domestic violence complaint for either side. It merely would show that someone was getting information to see if the reasons for the complaint were reasonable to pursue a case or if one had to mount a defense.