Are you actually going to court though? You won’t be able to go to court without trying mediation first and that needs to happen where the child lives anyway. Mediation should address whatever the issues are. And is that three hours by car or train or round trip? The thing is all things being equal he may be entitled to joint parenting (providing it doesn’t affect schooling), or at least regular overnights. If it’s three hours to you and three hours back, that’s six hours out of his parenting time just spent travelling. It might be arranged that you meet halfway. But as I say it depends what your problems are.
Thinking of it coldly without knowing the facts, it’s not fair contact for him if he – for example – drives for three hours, gets about two hours contact tops (presumably spending money to take her out somewhere?), and then drives all the way back again, once a week or whatever (and all at his cost). Or can he stay with you? Or are you expecting him to get a hotel at his own cost also? Any contact expense will be evaluated against what he gives you on maintenance. A court has the child’s interests at heart not yours and at the moment, it sounds like a couple of hours a week with all the time and costs attributable to him is not fair on the child as it is going to prohibit contact.
A couple may not get on, or having split realise that money and locations are a problem, but that’s not the child’s fault, and a child needs both parents in its life.
Unless there’s something you’re not telling us?