A custody determination is made in the best interests of the children. The facts that you list are but some factors the court will consider when making that determination. However, based on the limited facts that you have supplied, there is absolutely no reason why a judge would separate three siblings that are 4, 1 and 4 months old. It is highly unlikely. Now if the childen were much older and one had a preference to be with dad over mom for some reason, then I could see a split of the children, but not under your facts.
Custody is determined by what is in the children's best interest, an both parents start on equal footing. You should set up a meeting with an attorney who practices family law to discuss your circumstance and who can advise.
That would depend on what the court deems to be in the children's best interests. Among other things the court will look at who the children's primary caretaker is and if they are thriving under that persons care. Also, generally, the court does not favor splitting up siblings unless there's a compelling reason to do so
The short answer is yes there is a chance. Custody is determined on the basis of what is in the children's best interests. Lots of things go into that consideration. A consultation with a divorce attorney would be appropriate.
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