Travel while MN1 under process

I applied for my 2 daughters aged 2 and 4 in July through NCS, biometric submitted 1st of August. In October I was going through the documents and spotted that the biometric invitation letter for my older daughter had incorrect DOB for her, instead of December it had November on it. I called The customer service and I was advised to write to nationality team and biometric team. Sent emails on the 23rd of October to both departments, nothing heared since.
I called again last week and I was told that they've recieved the email and we will get another bio invitation letter.
Now the situation is that we've are flights booked for the 1st week of January.
I hold ILR and my wife is on FLR M. Both the daughters have American passport with no valid visa. There MN1 applications are under process.
US passport holders don't have to apply for visa to UK, however in our situation do you think would there be any issues at the airport upon our arrival to UK?
Sorry about the long post. Look forward for your valuable inputs.
Many thanks
Zaidi