Are there any options if I cannot fulfill the UK residency requirement?

In the scenario you describe, it may be a better idea for your wife to be the Main Applicant, with you as her dependent. If she is able to spend five years in the UK for at least 185 days each year, then she can apply for settlement after five years. As her dependent, it should not matter that you have spent most of your time outside the UK. There is no residence requirement for spouse dependents in the settlement application.

There are presently no residency requirements under the Tier 1 programmes (Investor and Entrepreneur). It would probably be best to put the application in your wife's name, giving you the flexibility of travel.

Based on your scenario, your spouse can be the principal applicant with yourself and the children as accompanying dependents.

You are correct that your counsel may explore the possibility of having your wife as the lead applicant instead, however you would need to discuss if she is eligible. Your counsel will also need to assess your financial circumstances, immigration history, procedure, and future to ensure the prospect of success.

For ILR, it is important to spend at least six months in the UK each year. Although, if you do not want to obtain ILR, then the residency requirement does not matter. For British citizenship, there is more flexibility in respect of your absences from the UK and the Home Office will look at the reasons for the excess absences and have the discretion to disregard compassionate personal trips or business trips.

Tier 1 investor visa application is the route for high net worth individuals who have established themselves and have €2 million to invest in the UK economy. The genuineness of the applicant will depend on many factors which the Home Office will consider before, during and after the granting of the initial visa, the extension, and permanent residence.

The application should be made in your wife's name as the main applicant. Only she will, therefore, be required to meet the residence requirements for the purposes of ILR but not citizenship should you wish to apply for this at a later stage. This is clearly not a comprehensive response and you should take detailed specific advice on your circumstances.

Yes. If you cannot meet the 180 residence requirement, you should have your wife apply as the main applicant as the whole family will be able to obtain indefinite leave to remain on the basis of her residence. This is the case even if you spend very little time in the UK. Have you already opened a UK bank account? I would recommend seeking experienced counsel to help with the bank account and in preparing documentation for this process.