The claim comes after Lampard's model ex alleged on Twitter that the couple deliberately prevented Luna, 6, and 4-year-old Isla from contacting her at Christmas.
"Sad a father would deliberately stop his children from speaking to their mother over Christmas," Rivas wrote on Christmas Eve. "You would have thought the girlfriend would have a little maternal understanding."
Insiders have since insisted that Rivas confused matters by failing to take her mobile on a trip to New Delhi and was denied access to the children after allegedly calling at 3am.
"Frank and Christine were delighted to have the children for the whole festive period and have been having an absolute ball," a source told The Mirror.
"Christine's been spending an increasing amount of time with the kids. They adore her - and vice versa. They've taken to calling her 'mum', which is incredible - she's so touched.
"Frank received a text from Elen informing him she didn't have her mobile on her, but could be contacted on this other number. It was all pretty odd.
"Elen rang to speak to the children at 3am on Christmas morning, which wasn't exactly ideal... When Christine read Elen's Twitter comments she was understandably incensed and incredibly frustrated."
A source close to Rivas responded by saying that she had been determined to speak to her daughters on Christmas Day.
"[Elen is] happy for Frank to have the kids this Christmas as she had them last year," they added.
Lampard proposed to Bleakley back in June. The footballer broke off his engagement to Rivas in November 2008 after a seven-year relationship.