While in the crisis my therapist told me.. When you go to make a decision and you waffle, the answer is no. She also noticed depressive symptoms were on the rise and to get a med check. This way the symptoms are stabilized so I can make good decisions. Then there's always the 48 hour rule. If it's a good idea now, it will still be good in 48 hours.
Are your boundaries severe? Only if the other kids don't want to be included. Only if it's not a safe or positive place to be. Only if you feel it is morally and ethically wrong. Only if you think it sets the wrong example for them to be around the girlfriend.
I know a divorced woman who had three kids, had a rebound marriage, found out she was pregnant just as her second divorce started and married a third time. The father in the second marriage is involved solely with his biological son. I don't know if she instituted it or because the second marriage lasted a year and the kids didn't bond with him.
It comes down to what works for you, what your goals are, what you need.