If you and the other parent cannot agree on the child arrangements, and this includes on matters relating to medical and travel, then you are supposed to try mediation as a first port of call; you will need to attend a MIAM at the very least before applying to court.
If mediation is unsuccessful or the other parent won’t engage, the mediator will sign your form and you will be able to apply to court for a child arrangements order. It is also possible, on the same form, to apply for a specific issues order to be allowed to take the child abroad without the father's consent - however as this application can be achieved with a child arrangements order, the court may not make that order - but you should apply for both (on the same form) just to make it clear what you are after.
Unfortunately the court is not likely to limit his parental responsibility so they are unlikely to dispense with you needing to confer with him over major decisions such as education and medical care, but that is something you can discuss with the judge.
You apply for both orders on form C100, and the cost is £215 unless you are on a low income or benefits in which case you may be entitled to fee remission, see form EX160. The court will make a decision based on the best interests of the child.
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