This is hard. Seems to me that you need her for two reasons. You need her to be your partner and you need her to be your friend as you grieve. From your description she sounds like she's either not sure she's poly (is she replacement planning?) or she can't handle the demands of NRE with the needs of her current relationship. The latter is admittedly hard under good circumstances. Whatever the cause, expressing your needs and going beyond that expression to work through specifics you both can agree to is important. Work through the implications of your needs so that you can get to things you both want to do differently.
Since you asked for practical advice, here's my view:
I would suggest that you set aside a good amount of time with your partner to work on your relationship. When you have kids, the time together can often feel more like work than play. And, her time away with her new person has that added sense of freedom that gives the NRE a little top spin. So, finding time to date your partner sans kids is really important. Make it regular and balance it with appropriately with the time she spends with her new partner
Finally, with all that, it's easy to forget the kids
So, make sure you also find time to plan family moments together. Reinforcing the "fun" parts of being a family that goes beyond the daily grind is equally as important.
This is why poly is so damn hard. It's not only an emotional mindfield, it's also a huge planning challenge. Need more time and energy in the week to try to it all.