If there is no court order in place, then on what basis is your husband saying that you don't have an entitlement? From a tax perspective, if you provided more than 50% of the support for both, then you have a tax right to claim them both. If you received a refund sum, compare that to what you'd lose out on as a refund if you filed with one child as a dependent. That savings is what you're really fighting over. If you're benefiting by $3,000, that just might be worth calling your husband's bluff to see if he really tries to take legal action. If he does, it seems unlikely that you will be forced to amend a tax return if there is nothing on an order about who takes the deduction. Regarding the taxes, you're supposed to deduct what you pay. If you paid 100% of the house taxes, then you're entitled to that deduction.
The parent who has physical custody more than the other is entitled under federal tax law to claim the children as a dependent and all that goes along with that. If his average is 20 days a month, he had them more than you and is entitled, absent a court order to the contrary, to claim them as dependents. You should discuss this with your divorce attorney, and it looks to me like you should except his proposal.
I believe the earlier answer addresses the correct tax analysis based on the Internal Revenue Code.
From my perspective as a matrimonial attorney, I believe you should discuss this with your attorney prior to filing the returns. This time of year is always filled with questions about taxes. There may be other factors involved in your particular case which are germane to a determination of this issue. Perhaps your respective attorneys can negotiate the various deductions and exemptions to which you may each be entitled this year and going forward.
Regardless of whether you already filed your taxes, you should consult with your attorney and determine how to proceed, before your husband does so and your attorney receives a letter from opposing counsel about this issue.
The content of this post is not legal advice and should not be relied upon as such. I am not your attorney and no attorney-client relationship has been formed based upon this exchange.