Am I obligated to give up ~$100K in my share of house equity to wife for the reason of providing stability to kids?

Your counsel should advise you, but if you are asked to give up 100K in equity, you should receive some monetary offset.

It probably isn't reasonable but there are many other factors that need analyzing. The court could delay a sale and/or division of the house to protect the stability of the children but it wouldn't order you to give up your CP share in the house to protect the stability of the children. A court order to delay or defer sale of the home would be what we call a Duke order here in California, but again, it doesn't call for you to give you your CP share. You need to seek legal counsel from a skilled family law attorney.

There are several ways of handling the deferral of the sale of the family residence but none require you to give up all or even part of your equity in the home. If the issue is left to the court, there are a number of factors the court must consider before making such an order. Those factors are listed in the statutes governing such deferral orders and are set forth at Family Code sections 3800 through 3810. As you can see if you look at these statutes, we would have to be provide with a lot more information than what you have given us here. You need to take a look at these statutes and think about your family situation. We see clients all the time who insist they are going to keep the house and they often want to use the excuse that it will be stability for their children. We see people who insist on keeping the house because they hope to have an advantage in child custody matters either because they think the court will be impresses that the children will be in "their" home or they believe their older children will insist on living with them so they can stay in the home. Very often, the one who wants to keep the house cannot afford the house even if the other spouse is willing to wait for their share of the equity. You need an attorney to help you so you are not coerced into something that may be very bad for your children. If both of you are concerned about your children's stability perhaps you should explore whether ending your marriage is a good idea. You need a lawyer.

Your interest in the house is yours. The court's obligation - by law - is to divide the marital property equally, or as equally as is practical. If your children are of the age where a deferred sale of your house is appropriate (which is not, at all, a given), then your claim to the equity is not extinguished. You COULD take a promissory note from her, and record your judgment with then County Recorder's office, which would give you a lien (like a Deed of Trust). You and your lawyer need to do some creative problem-solving. if you don't have a lawyer, then it's time that you change that, as too much is at stake!

There are other ways for her to stay in the house. You should not give up the equity, but instead work out a solution.

No. Courts are required to divide the community estate equally. She can sign a note (guaranteed by a deed of trust) and make payments. Just one idea, there are other options.