Children traveling between parents - BRP question

[ambhyr]

Backstory:
I and my 2 daughters (all three american citizens, girls 9 and 11) were granted LTR in April, as i married a British citizen. We all three received BRPs. My daughters have to travel back to the US 4 times/year to see their biological father. There was a very long, expensive and nasty court case (brought about by him) to prevent them moving and much trust has been lost in the co-parenting relationship.

Question:
Is there any circumstance in which my kids can travel with just their passport (which contains a now-expired vignette) and enter the UK with that? We are VERY reluctant to give my ex possession of the only cards which prove the girls' right to live in the UK...we fear they would be "lost" when it is time to come home and put us through repeated expense and replacement requests throughout the year.

If my husband and I were waiting right on the other side of Border Force with the BRPs, is there any circumstances that would allow us to show the BRPs for the girls even though we aren't traveling with them? I can't find a contact number anywhere for Border Force to explain the situation and our concerns and see what might be done to protect against it until the children are old enough to hang onto their BRPs and Passports themselves.

Most appreciative of any advice, even if it is just that there is no way around it. I know there are processes and controls for good reason, but you dont know if you dont ask.