I hate to say it but I think you are being quite unrealistic about the amount of contact the courts will allow. My DHs ex had similar ideas to you, I think. She would only allow very limited contact under very specific circumstances.
I realise you are only a few short weeks post-birth, but you need to come to terms with the fact that your LO has two parents, and unless you can prove that your ex is a danger to the child, he will be granted unsupervised contact very quickly, followed by full days and even overnights.
We had no option, after two years of being messed around, but to take DHs ex to court, prior to this he'd been allowed two hours of supervised contact approximately once a month, always on her terms and at his expense. SD was 2.5, he was in court in June and had unsupervised contact in August, full days in October, and overnights in February. It was supposed to be overnights in October.
I'm so sorry you are going through this at a time that is difficult in any event, but you have to understand that, yes, you bore the child, but it is not just your child, it is your ex-partenrs child also, who we can only assume was concieved in love. This child has a right to know all faceats of its family, it has a mother and a father, aunts, uncles, cousins and grandparents, who all want to be part of its life, and get to know the child and love it.
Contact will be granted to the father, unless you can provide very good reasons not to, and during his contact time he will be able to do as he wishes. I know some people believe this includes dumping with grandparents, but my SD loves her Grandma and it is only right that she be allowed to spend 1-on-1 time with her, the same as her first cousins and half-sister do. This is not 'dumping' her but allowing her form normal, healthy relationships, as a normal child should be allowed to.
Courts are very much on the 'side' of the child, not the mother or the father. If it goes to court, they will decide what is in the childs best interests, taking into account both sides. You said in your other thread that you were allowing 45mins a week, and this was regular. 45mins a week is not enough to build any sort of relationship, you need to work out with your ex a way forward, and a way to build up time for hime and you LO, as you risk looking unreasonable in court.
I wouldn't even consider breaking any court order, the sanctions came be quite extreme, even as far as residency being given to the parent most likely to allow reasonable contact, this is not always the mother.