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It is likely the Support Case can be transfered or merged into the Probate Case so you child can claim against his statutory share of the deceased's estate (provided the child was not named in the will)
Did the executor contact you? When did the deceased pass away? Have you filed a claim against the estate?
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Why not hire two attorneys, each specialized in their field? If an attorney charges an hourly rate, paying a probate attorney to do both will take the probate attorney, for example, 30 hours to work both cases. If you have the probate attorney do the probate portion, he will take 6 hours, and your litigation attorney can handle the other part of the matter in less time than a probate attorney could have.
I would definitely speak with a probate attorney and there is a chance he has experience in civil litigation. But find someone you trust, because most attorneys will say that they can do it.
I hope this helps answer your question.