First, we need to be clear about what you mean by "estranged spouse" and what you mean by "inheritance." I'll assume that you are still legally married but are living
apart and may even be legally separated. I'll also assume that the "inheritance" has only been received by you after you stopped living together.
Second, the precise answer for this question will depend entirely on the law of your particular state. In some states (such as California, a community property state) inheritances are never shared legally with the spouse, as they are always the separate property of the one who receives the inheritance. In other states (i.e. the non-community property states) the courts have a bit more leeway in answering this question. And, each state has its own alimony and child support rules that may come into play here.
Third, speaking in the most general terms, the rules are likely to be as follows:
1. Your inheritance will likely be considered your own asset, and the default rule is that you won't have to share it with your soon-to-be ex-husband.
2. If you live in a non-community property state and have not completed your dissolution process yet, the judge ruling on your dissolution can take your inheritance into account when dividing up the marital assets and debts (the non-inherited assets you each racked up during your marriage). In most equitable property states (i.e. non-community property states) there are a set of factors that guide the judge in making this determination, and "financial need" is one of those factors. Thus, if you now have a greater abundance of wealth you may not need to retain so much of the family savings or the equity in the family house. The judge is allowed to take that into account when resolving any disputes about other assets. You should check with a local family law attorney who has handled cases like yours in your area, to see how the local judges approach this question, and you will want to take that prospect into consideration when negotiating a settlement with your ex-husband.
3. In just about every state your inheritance also can have an effect on any award of spousal support or child support -- even in a community property state. The concept is that the income off your inheritance (or the imputed income if you are investing it in non-income-producing assets) is a benefit to you, and thus you don't need to receive as much iin support (or, if you are already the richer party you can afford to pay more in support) as a result. As with the asset rules, you should check with a local family law attorney to learn what the rules are in your particular area for this sort of question.
I'm sure you are not going to be eager to share your inheritance with your ex, and most likely he won't be entitled to much of it. But you probably will have to disclose it as part of your divorce proceedings; your goal should be to keep the "sharing" to a minimum!