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Warring parents who refuse to comply with care arrangements could be fined, jailed or forced to carry out unpaid work.
The proposals have been revealed in consultation papers which aim to strengthen children's rights to maintain contact with both their parents when they split up.
Children's Minister Tim Loughton told the BBC: "If parents decide to go all the way to the courtroom after they split to decide what happens to the future of their children... then it should be made very, very clear, before they go into the courtroom in law, that playing the sort of winner takes all game that many parents have done in the past - where one parent can be completely excluded from the life of that child - is just not going to happen."
The Government is consulting on amending the Children Act 1989 to enshrine shared parenting in law.
Under the plans, family courts in England and Wales must assume the child's welfare is best served by remaining involved with both parents.
Ministers believe this will encourage more separated parents to resolve disputes out of court and agree care arrangements that fully involve them both.
"Children should have the benefit of contact with both of their parents through an ongoing relationship with them," the documents say.
"This is why we are publishing proposals today setting out that, where it is safe and in the child's best interest, the law is clear that both parents share responsibility in their upbringing."
However, ministers said parents will not have a right to equal time with children.
Family law expert Prof Liz Trinder warned the change would make it harder for courts to focus on child welfare. And campaign group Fathers 4 Justice described the plans as "vacuous".
Professor Trinder told the BBC that in around 99.7% of cases which went to court, judges ruled that both parents should have contact with their children. In the remaining cases, there were almost always "extremely good reasons" why one parent should not have access, she added.
She said: "The beauty of the Children Act, I think most people agree, is it's a very clear and simple piece of legislation and it just focuses on what's going to be right for this child, that's the only consideration for the court. Once you start adding in other principles, then you're diminishing that focus."
Nick Woodall, from the Centre for Separated Families, welcomed the Government's proposals.
"There is a problem in that far too many children are missing out on those vital relationships with both parents after separation," he said.
"The children who fare best and adjust the most easily to life after separation are those who are able to maintain meaningful relationships with both of their parents."
What do you think about these proposals?