Can I See My Children If My Wife Will Not Let Me?

Yes, you can if there is no restraining order, or order of custody. Before a divorce custody is supposed to be divided equally. I would go to the court and see what you might be able to do about this, talk to a mediator if you can. Hope this helps you out.

My ex wife is telling me that I'm only entitled to see my children for two weeks a year is that correct or just a lie

Yes you have the same rights as her because you are married, see a solicitor and the can get the ball rolling. Hope you get it sorted out

I would say yes.  If you are separated and there was no kind of abuse involved.  Then I would get an attorney which she is probably going to do anyway and go from there and try to see them so she don't use that against you.  You may also be able to go through someone else, possibly a mediator but I would for sure get an attorney also.
If you owe child support that is a different issue.  Usually child support would have to be caught up in some instances.  As long as there is no divorce decree stating who has custody etc.  Then I would make every effort possible to see the children.  They need both of you. 
Make sure you stay in the child's lives.  No matter what, and if there was abuse get help.  Also, try family counseling etc.  Good luck.