advice on inheritance planning

I'm not sure what you mean by the trust has been "imported" into the UK.  Before my family's move, we consulted with top firm tax consultants which including their legal department.  They have many international clients that deal with this all the time. 

The reason my assets are in a US living trust is to ensure my assets do not go through probate which is an expense and are inherited by the heirs I have designated. 

I probably should add that all my assets are in the US except for a few bank accounts in the foreign countries I have lived in and the UK.  No investments outside the US. 

I believe the rule on where an individual is domiciled is what impacts inheritance tax rules.  I have one friend who is reaching the max to be still deemed non-UK domiciled and plans to move back to the US. 

Depending whether the UK is your domicile, what US state you have assets in, what nationality your heirs are, as well as how much assets you have, impact the right decision on how to plan your estate.  Thus, seeking legal and tax counsel is a wise thing to do.

I am not clear which international tax consultants you spoke with. When you have digested some of the discussions below; you'll appreciate why this issue needed highlighting. Hopefully, you have counsel's opinion in writing. I don't know the extent to which you might be affected, but this issue (in particular with California based living trusts) is widely known, not new and can be extremely fact specific.  Trying to fit California (or other State specific) focused advice into UK law is often dangerous. In no order at all; these are the first hits on Google within a few minutes of searching; but there are dozens of other discussions which are easy to find given a little more time:
https://www.boodlehatfield.com/the-firm/articles/the-pitfalls-of-usuk-tax-planning-the-us-living-trust/
https://www.burges-salmon.com/news-and-insight/legal-updates/the-dangers-of-us-lifetime-trusts/
https://www.frankhirth.com/images/uploads/resources/Trust,_Estate_and_Family_-_brochure.pdf
https://www.michelmores.com/news-views/news/usuk-tax-%E2%80%93-basics
https://2vl13w4d5y6l3w9ia52p3av9-wpengine.netdna-ssl.com/wp-content/uploads/20111109_watson.pdf
http://trustsdiscussionforum.co.uk/t/us-living-trust-is-it-a-bare-trust-for-uk-tax-purposes/2075/5
http://www.nysba.org/WorkArea/DownloadAsset.aspx?id=62108

I am getting more confused. So trust for US citizen who is living in UK for a long period is problematic.

What is the best way to transfer my assets to my children than? My kids are very small (<7) and my parents will never be able to understand UK/US tax issues,  or even be able to track my UK and US retirement, investment and bank accounts if sthg happens to me and my wife.

Does the will help at all? I am not even sure about this anymore, since anyways if sthg happens to us we want our children to be distributed with the proceedings.

All we want is somebody who is knowledgable in both UK and US inheritance to help the children out with all the paperwork and dealing with taxes so that they dont end up paying double taxes, and get access to funds they might need right away...

GUYA posted some great articles on the topic.  I read through some of them, and it is clear that estate planning can be really complex if you live abroad.  Many factors (heirs, citizenship of heirs, amount of assets, domicile status, . . . ) all impact the best solution to estate planning. 

A US trust for a US citizen living in the UK can be problematic.  Whether it is or not is dependent on many factors - wording of trust, if you are UK domiciled or not, if the trust was created before you lived in the UK or not, how long you have lived in the UK, and the list goes on.  That's why it's important, in my opinion, to seek legal and tax counsel on how best to plan YOUR estate. 

In your situation, you should at least document your US assets so your family knows what you own.  Make sure your beneficiaries are listed on all accounts. Children can be listed as secondary if you have someone else listed as primary such as a spouse.  If you have a financial advisor, consider giving him or her that information too.  My family knows that if anything happened to me and my spouse, they should contact my financial advisor who has a copy of my living trust and list of assets.

Given how young your children are, it is also important to document who you would like custody to go to and if possible ensure your family will have the financial resources they need - consider life insurance. 

GUYA posted some great articles on the topic.  I read through some of them, and it is clear that estate planning can be really complex if you live abroad.  Many factors (heirs, citizenship of heirs, amount of assets, domicile status, . . . ) all impact the best solution to estate planning. 

A US trust for a US citizen living in the UK can be problematic.  Whether it is or not is dependent on many factors - wording of trust, if you are UK domiciled or not, if the trust was created before you lived in the UK or not, how long you have lived in the UK, and the list goes on.  That's why it's important, in my opinion, to seek legal and tax counsel on how best to plan YOUR estate. 

In your situation, you should at least document your US assets so your family knows what you own.  Make sure your beneficiaries are listed on all accounts. Children can be listed as secondary if you have someone else listed as primary such as a spouse.  If you have a financial advisor, consider giving him or her that information too.  My family knows that if anything happened to me and my spouse, they should contact my financial advisor who has a copy of my living trust and list of assets.

Given how young your children are, it is also important to document who you would like custody to go to and if possible ensure your family will have the financial resources they need - consider life insurance.

Just in case it helps to say; here in the UK a barrister is known as counsel.  A solicitor would instruct counsel. Many people might want counsel's opinion on things where more than one possibility might exist as to how a court might interpret a structure or law is unclear.