In this situation I think the court would say no.
I asked my ex (no family in the area) if I could relocate and he didn’t respond. He had a house and job locally as did I and we both had no family locally.
I asked by letter formally and then via a solicitor he didn’t reply or to the next two letters, which a solicitor also sent. So I put my house on the market, applied and got a new job and got them into a school to start them in 14 days and they lived with family for the start of the relocation (difficult as you can’t apply for new school until you had an address in the local area etc ). The letters, applying and marketing the house took place over 4 months and he didn’t respond at all in that time. Not even to say ‘no’. Fortunately my solicitor had the sense to file a change in the court order etc with all the correspondence etc and details about the ex who hadn’t seen them for 4 months at that point because he hadn’t shown any interest, about 6 weeks before the planned move.
My solicitor said even at that point house of market, I had resigned etc that we ran the risk of a court saying no. I offered two face time calls a week and 5 weeks or more of holiday with him.
The judge was on my side only because he just hadn’t responded to the legal letters up until 4 months after I asked him to move etc it still was very stressful and involved two court hearings. I had emails to him asking him for an answer as I had another job offer and needed to resign etc and in over 6 weeks he didn’t reply. He only responded when he got the legal documents for court order change. It cost me over £10,000 with solicitors and barristers etc
In your case, I doubt it. He is having contact and is settled and you do not have a new job - in my case I got a promotion and the children went from inadequate to outstanding schools and an hour commute to 5 minutes etc etc
My solicitor said ‘basically the court will say no to any relocation’ that is what you assume.
Why should he agree with less contact and be forced into a potential move or less contact because you want family support? You could get that over the phone.
Better arguments with your ex are retired parents doing the school run - but you ex is working from home he might be able to, or you. Do you work full time? He might go for it if you offer more contact in the holidays? I wouldn’t if the situation were reversed.
You could ask him if he would be willing to move near your family and get some family support and have 50/50?
I am assuming unlike mine, yours is having a good relationship with the child etc
Also how far we talking? I wanted to move hundreds of miles. 30 miles a court would agree I think - out of county I would go with highly unlikely. Same for changing their schools.
For me a big factor was local secondary was inadequate and new one was outstanding. Judge was interested in that too and the short commute for me to work, the family etc At that point my ex has contact Friday to Monday from school EOW but hadn’t taken that offer for 4 months. He only recommenced contact once he had my application to the court to move.
Try to ask your ex what might work? If he says no it’s a no.
Not ethical but one of my children’s friends mums was having problems in her marriage and wanted to relocate and knew he wouldn’t agree, but he liked her home area and parents and wanted to work on the marriage so they sold up and moved on the basis they would do all the school runs etc and they would work on their marriage etc. she admits she had no intention of this. They moved and got the boys into the local outstanding primary and then she said she wanted a divorce. I don’t agree with what she did. Be upfront in my mind.
Try to find a solution with him.