Not really the point of your post... but isn't that awful having to supervise the visits yourself? That sounds like a special kind of torture to me.
Not related to me, but my exH has supervised visitation of his younger kids (not mine). He has a list of approved people who are allowed to supervise (his family members) and he's not allowed to phone the kids.
I'm not really involved, but I thought phone calls came under the same category as supervised contact?
I've always found knowing the legal position, even if you don't do anything with it, to be really helpful and strengthening when needing to put a boundary in place. Lots of solicitors give a half hour free.
I haven't used my divorce solicitor to represent me in a decade, but if I have a question, they still have my file and are happy to answer the odd question on an ad hoc basis if I just pay them for the time to discuss. I've found knowing where to go for advice to be so helpful over the years. Makes you feel like you have back-up.
Maybe you could just make contact with a solicitor, have your first free half hour and ask them this question as part of it? As kids get older it gets more complicated and more stuff comes up. It might be good to have a good solicitor to reference who has the background on file? A solicitor's letter is often a good way to terminate a dispute.
It is a parenting decision, but parenting with SS involvement and supervised contact is a different kettle of fish. You have to be careful, I once had it suggested by SS I would be seen as not protecting my child adequately by removing contact fully enough if I didn't take certain actions. My child is of an age where court orders etc wouldn't apply anymore, but I'm still careful to take the correct decisions as an outsider would see them.
Anything which can be enable contact you're not aware of should be really carefully considered.
Also, yes awful to give kids that young phones.