Yes, you can file for dissolution of marriage if you are pregnant. As for time-sharing, if you are breast feeding, a court may require you to provide milk to the father when he has time with the child. You should hire a local attorney who has appeared in front of the local judges, because he or she may know their tendencies.
JMP Law, P.A.
Juna M. Pulayya
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Although I am not licensed to practice in your state, and will defer to the state-specific information already offered, I would add that there is nothing fixed and automatic about the custodial access your court will define. First of all I would urge you to not use the term "visitation" as no parent should be a visitor in the life of their child. Children deserve better.
Regarding the custodial access to be ordered, I would hope that the best interests of the child would prevail. That would include the ability to bond emotionally with both parents. Psychologists tell us that process is encouraged in a healthy way when both parents have frequent contact with an infant, even if that contact is brief. It can be helpful if the contact of the non-custodial parent occurs in the presence or home of the custodial parent, so it is particularly healthy for your newborn if you can cooperate to allow that contact. Frequency can be lessened and custodial times increased as the child grows and develops the ability to remember the non-custodial parent from one time to the next.
To start in infancy with something like an alternate weekend schedule and sending milk is far from ideal for the infant, as the non-custodial parent is not remembered, and the child has the sensation of being handed over to a stranger every time. Imagine the child's fear and anxiety in such a situation.
Best wishes for a favorable outcome that works well for your child, and please remember to select a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.