My suspicion is that your kids are just not okay with any gf at this time. It’s most likely all too raw for them and her presence alone may be too much for them given all the changes in their lives. This may be what they are trying to communicate.
Me 41, H 47, M 15 yrs, S11, S13 BD 1: 11/4/14 we work on it; really I pretzel myself BD 2: 3/31/15 H goes down to "dorm room" 8/15: H back to MBR 10/15: H back in dorm room 1/18: H files, now divorced