If I may give some advice, I have seen these pattterns of denial and pulling at children like they are objects and not capable of human conditions. The BEST way to go about this is not FIGHT about the baby which was concieved during a time when both parties consented but unfortunately we're immature to handle the obvious implications should a pregnancy occur. You are both too immature to realize just how important and serious the consequences of family confrontations and separations affect your child upon the upcoming months and years to come. Being a father and mother are an important part of your lives now and if you intend on doing thing's right for your child, DO NOT start off by threats and denying that this took place.
First, your baby has a father-make sure it's on the birth certificate because your baby will grow and look at this important fact. Do deny them this as later it will be reflected upon and the implications do have there conditional response. If you had yours on there, you won't know what will happen to this child if you deny that because of anger or fear. They have a father and should know it.
Second, it's inconsequential who sees the baby from both sides, children need to know they have family on both sides that love and want them to be a part of their lives. Uncles, aunts, cousins whould all be available throughout the life and it's VERY important fro children to know that. Let all come together on occasions for whatever reasons and don't dread or deny their contact from both sides.
Third, you may feel indifferent right now towards one another but the fact is, you made this child, and despite your inner anger, you had affections for each other and will be fighting the need to be together for your baby for as long as you two live. It's a fact couples try to denounce this only to find these feeling's surfacing when as you mentioned, either of you try to have a relationship without the other. He want's to be there when someone else is, you will want him to not let the baby feel anyone else's motherly instict except yours. Both times are troubling to both of you. Give some reflection of what's really happened. You could be together and be the proud parents of this child enjoying all the holidays and special trips families have together. Don't rush into other relationships trying to forget or let anger play a role. Really think if you still might love each other and could this be the only mistake you make ( being apart ) concerning your lives and this childs future. Seriously think about that.
Fourth, accept the fact that you will be dealing with one another, whether your togthter or not, and make all negotiations between you emphasize the needs of your child first and accomodate each other. These years will be tough on you as a mother and the need to have sitters that are family will be beneficial to you both and your mother who is working AND helping you also. It may not be right now but later on you may wnat some freedom and either of you will not be able to be there for one another. Let everyone help who can. Also, get to know the families. It will help if you all get along and know who can and is willing to help should anything be necessary.
Fifth, it is not easy financially yet most parents that experience teen pregnancies often inflict emotional damage on both sides operating like go-betweens or talking what's best but all the while the one's affected with the decisions are not allowed to make them. And they sometimes use their power of manipulation to make mothers or fathers do thing's against one another when they really don't want to hurt each other. It's a child but some take this as a personal conflict of interest if say you (baby's mother&father) start doing thing's together with this child. The point that,"I'm helping you raise this child and taking care of you so I get a say in everything!" happens quite frequently. Try to make every effort that when decisions are made-both of you make them without influence from other family members because you'll have a guilt free life desiding what's best at certain point's for this child till adulthood. Be open for opinions but reationally take the point of MAKING the actual decisions regarding everything.
Sixth, I've said this in many different circles and it's difficult for some but, SEX should be approached responsibly from now on and expect throughout your times to experience difficulties restraining from it. If you know or not, it's very easy to get pregnant again after childbirth. It's also easy to think you can have another if you don't feel the financial hardships you would normally feel if you we're BOTH on your own at the time this child was concieved and born. Whether you know or are not sure on whether you'll have more children, make certain to stay on birth control now and deside to better the life you have now with this one child. Relationships outside of this childs life will have an affect on it's feeling's. Thinking someone else will fit in where their is a vacancy will never work because it's a battleground for more confilcting issue's to arrise. Try to make sure your not compelled by lonliness to run to find another willing male to take the place right away. Sometimes you'll be torn with these feelings so that you'll have companionship and someone to help you-and the baby will have a father-all together like it should be. Just be weary of this and you'll know how to handle this with talking to someone.
Parents: Your son or daughter had a child. They are both responsible for the upbringing of this child. Teach them the skills that give balance to a good life going forward and let them know your not against either of them. This child needs to know there is a mother and a father that concieved through love. Even though their immature now, time will grant experience to know their feeling's towards one another and no one want's to be left out for making thing's tough while their apart IF they get back together. Which happens quite a lot if you have not seen this trend. Be Switzerland-always be there for either if needing counseling or guidance.
Your grandchild will be glad you did this and you will be too at the most important times of their lives.
I leave you with this-I hope you realize I'm just a dad and want to help you where my experiences have given me these good examples I've given to you as advice. So trust me when I say, you can't have a do over-this is for real-make it the best now and forget the past. You'll live better overall.