I do not think you should be seeking a SRO, instead I think should you be going for a variation (change) of the exisiting contact order.
The first step would be a letter to the ex or her solicitors if represented. The aim of the letter is to present your proposals and seek some common ground. A necessary step. You want to demonstrate that you have at least tried to deal with the ex out of court, and, anything you can do/say now to reduce her opposition to your proposals is worthwhile.
If the final order is less than 12 months you would use the C2 court form. If over 12 months then it''s another C100 form. The order you would be seeking would be a variation to the exisiting contact order. On the form you would keep your reasons very short...you have moved much closer to your dtr, have a wish to parent her more frequently, sadly you and the ex are unable to reach agreements.
It would be sensible to prepare a brief position statment for the first hearing outlining what changes to the order you wish and the main points you wish to get across.
May I suggest contacting fnf for further advice and support.
Ok...well, I reckon the order you need is a contact order, not a SRO. Not everyone would agree with me so you need to take advice and form your own view.
The court form you need (for either order) is the C100 court form. There''s a tiny box for entering why you want the order..no statement needed at this stage.
As a litigant in person i personally feel joining families need fathers is the single most important piece of preparation you could do in that it allows you to access a wide range of support.
In parallel to the court stuff..sending a conciliatory letter to the ex offering mediation and suggesting ways you can defuse her concerns would, i reckon, be a smart move. In that it''s nice to be nice and you want to reduce her hostility and opposition if that''s at all possible.