If you are moving children away from the jurisdiction of the courts in England & Wales you need the consent of all those with PR for a child or permission from the courts. I'm not a solicitor but in my understanding is the courts have made it clear that generally it is inappropriate to restrict the movement of the parent with care within the UK unless they are relocating to somewhere inaccessible or there is a history of frustrating contact.
However, when children spend a substantial amount of time with both parents so that care is shared 50:50, or almost 50:50, a court may decide it is better not to disrupt education, established friendships or relationships with the extended family so order that the children stay the majority of the time with the parent who is remaining local.
In any event if no agreement can be reached with the father pre-empting a PSO by applying for a specific issue order for permission to relocate the children would be the reasonable thing to do. You would then need to show that arrangements for, living, education, finances and contact were well thought through and practical. Children's wishes and feelings are taken into account according to their age and maturity. Also the duration of your new relationship is important.
When parents live a distance apart it isn't uncommon for the loss of contact to be compensated with extra time during the school holidays. For example, contact might be every half term and half the other school holidays so that there is never a gap longer than 6 weeks. If the distance makes long weekends impossible it might be children spend two weeks of the summer holidays with the parent with the majority of care and remaining 4-5 weeks with the other parent plus the October break, half the Christmas and Easter holidays.
The non resident parent may apply for a variation to reduce child support due to expenses related to contact. Depending on the circumstances there might be an expectation that you assist with travel, although the effects upon your finances and new family are a consideration. When money is short it is hardly likely to be deemed in a child's interest to place an increased financial burden upon the family if the other parent has the means and resources to do the traveling.
It is worth investigating methods of travel. When my ex moved 400 miles away it was possible for our teenagers to fly down alternate weekends and booking well in advance was considerably cheaper than motoring costs.