Residence orders are now Child Arrangement Orders which are applied for using form C100. C1A is a supplemental form used where it is considered that the child/ren is/are at risk of various harms as outlined in section 9 of C100. Form C8 should be used to ensure that your contact details remain confidential and are not disclosed to any other party without a court order, however, this doesn't necessarily prevent human error.
Without knowing all of the facts of the matter it is not possible to advise here but, from your OP, you may be best advised to wait to see if the father of your dc makes an application as these orders are rarely granted without mediation having been attempted and you should be aware that, should it go to court, it won't be up to you to decide to "allow supervised meetings of my children with their dad once my kids are ready".
If you are concerned that the father of your dc may attempt to take them out of your care and control, I would suggest you apply for a Prohibited Steps Order alongside a Non-Molestation Order.
With regard to the non-mol, you should be asking the court to forbid the respondent to use or threaten physical violence against you, intimidate, pester, or harass you, from communicating with you or instructing or encouraging others to do so, and from attending your property.
Before you give consideration to making applications of this nature, please talk to refuge workers as giving the address of the establishment on court forms may compromise the safety of current and future residents.
Assuming that you have been placed some considerable distance from your former home, there should be no need to rush to court and this will give you time to consult a solicitor as to the best way to proceed so that the necessary orders are in place when you move into your new home.
For your bravery and with best wishes for your future happiness.