This situation you describe is possible, but is also very complex and can be rendered invalid by minor discrepancies between intent and action. I will provide some general info here, but I strongly recommend you seek specialist advice from international taxation experts before putting any of your plans in motion. Get this wrong, and it will be costly!
Where I have had to make assumptions, or where the advice is critically dependent on a key point, the assumption will be shown in bold like this.
Generally speaking, Directors and Owners of Limited Companies (or international equivalents) are recognised as employees of the company, for a variety of reasons, but usually including the fact that you are retained by the company in an employment contract.
You do not mention what legal status the NL entity has, or if it forms part of a group of associated companies, but if you would be ordinarily recognised as an employee (were you a dutch national), then the common approach is to structure your assignment in one of two ways:
A: You (employee) are seconded to the NL branch of the business, with the NL entity assuming all costs (including reimbursement of home country salary) and you would become personally tax resident in NL should you be staying long enough.
There would be a service agreement between NL and UK, clearly laying out the nature, scope and skills being contracted (amongst a number of other points) as well as the fees for delivering the service. As a seconded employee of the NL business, you would then be resourced into the fulfillment of that service contract. There would then be a dual tax liability (however a partial offset would arise from the Double Taxation Treaty in force between NL and UK) but again, you will need international taxation services to ensure compliance with both countries' tax legislation and the submission of tax declarations in both countries.
B: You (employee) are seconded to the NL branch of the business, except in this instance, the appropriation of costs is not as important as you do not work in or for the UK entity for sufficient days to break the Short Term Business Visitor legislation.
The STBV is a tiered declaration process that applies increasingly controlled compliance demands depending on how long in total over a set period of years you perform UK entity duties. From a simple written statement, right up to production of legal documents and payment of PAYE (income tax).
Warning: under the STBV, to perform UK duties you do not need to be in the UK or even have worked for "a day" for it to be counted towards the total - don't get caught out by this!).
Again though, I cannot recommend strongly enough just how important it is to seek professional advice - determining the legal basis for your visits can take more of your time and resource than the actual move would. But then, if it were easy, I would be unemployed!
I do hope I've been of some help, despite being fairly broad and assumptive. I'm more than happy to continue discussions and general guidance about this topic, just obviously not in a public forum, and also without personal data, for ethical reasons. If this would be useful to you, just drop me a line.