Would I be able to get custody of my children back?

You need to show what has changed since then and why it would be best for the children for a change.

Is it legal for me and my partner to have sexual images over Skype or snapchat

No no and no. This is a big problem for you.

Ex wants to increase my child support falsely claiming that voluntarily reduce her wkng hours to bring child to school?

If she is voluntarily working less, then she should not prevail in court.

Do I need a lawyer to get full custody of my son?

You will need an attorney to make the arguments for a change back to New Jersey.

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It likely would be subject to some percentage if assets were used or efforts diverted.

Could I not let my 4 year old sleep over her father's house because of sleeping arrangements?

You can raise that as an objection and choose to address it in court.

Credibility - Family Court Trial

A judge needs to make findings and conclusions.

Is there a time limit to amend the final decision of the judge in a divorce case?

You will have to file a special motion which has a one year time limit.

Is there any law, statute, or common opinion on unrelated, opposite sex children sharing a bedroom?

None but common sense should dictate the results.

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My husband would like to sue his parents for years of emotional abuse, and now Social Security Fraud by his father. How?

This is not a family law matter but one that should be discussed with a civil trial lawyer.