Unfortunately in England grandparents do not have any automatic rights, and therefore you cannot force your son to allow you tp spend time with your granddaughter without going to court - and if you decide to go to court, you will first need to seek the court's permission to make the application. I think that you would easily get over the hurdle of gaining permission because you have had an ongoing, involved, relationship with your grandchild since the beginning, and therefore the court would give you permission to make an application for a child arrangements order to spend time with the child.
As you currently have every other weekend, that would likely be endorsed by the court as in the child's best interests, unless there was evidence put to the court that doing so would be detrimental in some way to the child. In other words, it will be very much fact specific based on the child's circumstances and best interests.
Before applying to court, you will need to attend mediation - which is the best way to try to resolve things if you and the father cannot agree. Mediation is less stressful than court and with any luck an agreement can be reached for the child's sake as clearly having her grandparents involved is important. However, if it does not work, or the father refuses, then the mediator will sign your C100 application to court for a child arrangements order.
You will need to ensure you pay particular attention to section 5 of the form where it asks if you need permission as you will need to tick that you do and explain why. The court will deal with that part of the application first. The rest of the form asks what you are applying for - and the court will deal with that part once it has given you permission.
Cost to apply is £215, unless you are on a low income/benefits, in which case you may be eligible for fee remission. See the forms and how to find a mediator at the links below.
Find a mediator here: www.familymediationcouncil.org.uk
C100 form: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/946762/c100-eng.pdf
EX160 form: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/952045/ex160-eng.pdf
E160A Notes: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/958038/ex160a-eng.pdf