I largely agree with your stance, but I believe that the OP should not give up that easily.
The fact that the property is open is a security risk for both the vehicle and the child's safety and security. This risk is further increased due to the fact that the father no longer lives there. A responsible parent would need to secure the child's home and the vehicle, the vehicle is essential and the child indirectly benefits from it. The previous arrangement wrt securely parking the vehicle has been withdrawn, so the OP needs to take out a loan, based on the cost of a security fence / wall, and add it to the list of expenses that she incurs in respect of the child.
Maintenance court will split the expenses iro the child between both parents, based on income and ability to pay.
I don't know their, her and his, situation. The court will look at circumstances, and the gate is best argued in reimbursement. You have contested and uncontested divorces and each sets a unique course. She does have the option to seek remediation and that can be done through the court, and the courts are still open.
She wants her gate back, she needs to hire a pitbull, and you need to evaluate your own circumstances prior to going into lengthy remedial battles pending on how her ex reacts, and pending on their prenup and whether they do have a prenup will establish whether it is a good idea or not to argue property improvements. Our courts have new guidelines, they are encouraging people to reach a settlement. Pencil pushers, they will play it by the book, the same calculation sheets used by the courts and only the court will value the circumstances and that is only when you want to appear in court and this is where legal expenses can exceed your 'pay-grade', but you can do so without legal representation.
My only advice is to seek an interim order, get that executed, and then the ex will have no other option. Remediation is always an option, the ex doesn't play by the law have him arrested.
Most people who say the courts don't work, well, they either have the wrong arguments or they didn't actually go to the court. Legal counsel is an expense, but they can argue in urgency and with proper merit, and they will evaluate whether they can remediate with both parties. You also have people who run directly to lawyers, but then have poor experiences due to being unable to actually pay, and then they blame the court system. You can receive legal assistance through the court, those lawyers aren't that bad and there are top-level lawyers which are making their services available to those in need through this system.
Either get legal advice, acquire legal assistance or go to court.
