He needs to keep a diary of contact so he can accurately recall and show what contact he, and the dc, are used to and has been the norm for them.
I doubt she would take him to court over contact as she would loose and her sol would tell her that. It is far more likely that she would simply frsutrate or make contact difficult, or even stop it all together. If he thinks this is likely then he should be aware that the catalyst can quite often be when a new partner comes on the scene.
I would therefore suggest he looks at getting a formal agreement if he thinks it likely she will frustrate contact, whether the catalyst be divorce or a new partner or whatever.
If at all possible they should try and come to an agreement on contact. If they can't agree then he could suggest mediation as a way forward.
He could expect to see them for half the holidays and every other weekend if he took it to court, but that is not guaranteed, it just seems to be what the courts dish out as standard mostly. He can also represent himself at court which is a cheaper option if he feels confident enough to deal with the paperwork and speak in court. Court will want to see mediation tried first and will send them away for it. So he should offer (in writting) this first and they can get their agreement rubber stamped by the court rather than taking it to court if they can come to an agreement.
Courts do sometimes agree than midweek overnight when dc are in school can be disruptive and as they are putting the dc's best interests first won't order overnight midweek contact. However there is no need for him to have the dc at her house and he should in fact try and change this if at all possible. She can't insist he stays at her house for contact (though she may try to if there is no court order and say he can't see them unless it is on her terms).
How old are the dc? Could he offer to take them swimming after school, or to cubs/scouts/brownies and volunteer to help there if he wants to spend more time with them. Or even take them to the library or soft play rather than stay at Ex's house with them. Would she go along with that? Assuming he doesn't live too far away he could then move this to having tea at his house and bringing them home afterwards.
re the weekends - do they stay overnight with him? Does he collect or drop them to school? It is quite usual for a court to order every other weekend and this often includes pick up from school on the friday and drop off at school on the monday. So if he's only getting a few hours on one weekend day he could suggest they move to school pick up on friday and overnight till the saturday. Moving to the sunday every other weekend and then in a few more months moving on to the monday if the dc are happy with this. Again it depends on how far away from ex/school he now lives.
If she resists then ask why and suggest mediation as a way of resolving the issues. If she refuses to discuss, go to mediation and starts to frustrate contact then he may well have to look at court.
Court is not a quick fix, has no guaranteed outcome and can be costly, stressful and make the situation worse between waring parents. If at all possible avoid court, but it may be his only option if she is the sort to use contact as a weapon.
He shouldn'ty be scared of it though. Court will usually order some form of contact, even abusive parents can and do get supervised contact ordered.
So start by keeping the diary of contact and trying to do things amicably if at all possible. It's not always possible though.