There are no penalties, except you may cloud your title if it is done wrong. Your husband would need to sign the Quit Claim Deed. As far as the divorce negotiations, you need a good divorce attorney. The Deed situation could be handled in the divorce and the judge may order that your husband quit claim any interest he might claim as part of the final order.
A deed (of any kind) is a document which transfers ownership from one person to another. You should not execute a deed just because your husband wants you to. Before signing anything, you should consult an experienced lawyer in your area. For the protection of your children, you should talk to both your lawyer and your parents before agreeing with any settlement relating to your home.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.
You have many issues that need to be addressed. This is NOT something that you should do on your own, in spite of wanting to just get out and not have any contention, you have a responsibility to protect your children's interests. What many people (and a lot of attorneys) don't realize is that child support payments for special needs children do not need to end at 18 or 19, but can continue on depending on the needs of the children. If your ex is voluntarily underemployed, the court will not let him get away with it - if your attorney knows to argue that fact. For your and your children's protection you need to hire a good family law attorney who is conversant in special needs law. Good luck.
Carol Johnson Law Firm, P.A. : (727) 647-6645 : firstname.lastname@example.org : Wills, Trusts, Real Property, Probate, Special Needs: Information provided here is anecdotal and should not be relied upon or considered legal advice. Every matter is different and answers given here are general in nature and may not reflect current Florida law at the time you are reading this posting. Please contact me if you feel you need additional assistance with your matter.