Don’t put yourself on the outer, not with SD & not with his Ex.
She’s a child in your home, your rules apply. If your DH disagrees with them, then you need to discuss it, if not then ‘as you were’. Clearly with this your DH doesn’t disagree with you (and would go further), so you don’t need to do anything. However, I t might be helpful for DH to text/say ‘Paw has already told you DD will check her phone and can call you anytime she wants to. She’s left the phone on so that we hear any calls or texts & will get DC to reply when it’s convenient. If it was down to me I would turn it off while she is in my care. We do not want her glued to a screen while she’s here’.
Clear message that he supports you doing what you’re doing, your word is as good as his and that if she carries on, the result will be less availability, not more. Plus it reinforcing it its screen, not the contact, you’re both objecting to’
You’re not being unreasonable.
I can see why it’s nice for her to feel she can text/talk to her DD as and when, but she needs to respect her time with her Dad & you. She can still message her, she’s just needs to wait a bit for a reply. No biggie UNLESS there is ANY unknown background here such as DD not wanting to be there, being worried etc or your DH somehow being ‘less’ than he should be (but it seems unlikely as you seem too nice to put up with any of that crap).