I am getting remarried next month – and my accountant told me that, unless I get some tax planning advice and act on it, my children from my first marriage and my new spouse could end up at loggerhead

If you leave your assets, such as real estate, shares and/or the funds in your bank accounts, “outright” to your new spouse in your will, then your children from your first marriage would not be protected – since your spouse could do whatever he/she wants with your assets after your death.   If you leave your assets “outright” to your children, then your new spouse would not be protected – since your children could do whatever they want with your assets after your death.  In either case, the resulting dispute may end up having to be resolved by a court.
 
Tax planning, however, could benefit you, your new spouse and your children from your first marriage.  Tax planning, when utilized to create a tax-efficient estate plan, could involve the use trust(s) to protect both your children and your new spouse, such as (i) a trust established during your lifetime for the benefit of your children (which trust would continue to benefit them after your death), and/or (ii) a “spousal trust” established by your will for the benefit of your new spouse following your death (i.e. during his/her lifetime) with the remaining assets in that trust upon his/her death to pass to your children of your first marriage.
 
Tax planning, when utilized to create a tax-efficient estate plan, can also minimize (or at least defer) taxes which would occur on your death.  Tax planning can, and should, be an ongoing process – and provide enough flexibility to make any changes which might be needed in the event that circumstances change in the future.  A tax lawyer can help navigate you through this process and help you determine what is the most appropriate tax plan for you.