According to Doug's own filings for custody, he did not speak to the children after April 23. No one stopped him from speaking to them...that's just the date he gave as the last time he talked to them before Venus went missing.
He also claims that after April 27, Venus' family quit letting him talk to the children.
He didn't speak to the 5 yr old after April 23. It didn't specify the 3 yr old, so it looks like he did speak with her. And you're right - it doesn't say anyone denied him speaking with the 5yo after April 23. Just says that was his last date of contact with her.
In court records, Doug alleges that Venus' family has denied him a judge ordered daily phone call with their children since April 27, the day after Venus disappeared.
Doug says his last contact with his five-year-old daughter was even earlier on April 23rd.
http://www.wwmt.com/articles/margin-1376791-bottom-estranged.html
In general, I don't see a problem with the kids talking on the phone with him, provided there's coordination - perhaps through a children's counselor - on what they've been told about Venus and what should and shouldn't be said to them, and how to respond to any questions they may ask him about where Venus is.
The NG transcripts have either L or T saying the 5yo accidentally saw a news piece about Venus showing or saying Venus was with Doug and that she got scared about it.
Actually, writing this, I'm thinking supervised visits at CPS as he requests may even be better than the phone. There's no control over what's said on the phone, but I think a parent would be more careful over what they say in front of a CPS worker.
On the other hand, there are so many children of parents with conflicts of all kinds who don't watch what they say in earshot of the kids, so many parents who deliberately say negatively or potentially emotionally harmful things in earshot of their kids. I'd like all of them to exercise more control over their tongues lol.
My biggest concern about the children is Doug harming the children. I've read too many stories in recent months about a parent killing a child specifically to 'get back at' the other parent. This is a case where we can see signs of this risk, and I hope that the court will take measure to protect these little girls from harm.
ETA: I should have read ahead
Someone else already pointed out the 5yo/April 23 thing. Sorry.
