until you know what is happening and what solutions they are offering.
Why should they be offering solutions? It's not their problem to find solutions for.
The OP finds a babysitter or sits it out.
The MIL not knowing your DC is a good enough reason not to invite them IMO.
Some pp are far too dramatic over this.
From the update, it's clear that your MIL doesn't want to get too close for whatever reason. She's declined invitations to come to your house. Perhaps she wouldn't feel comfortable in your house and doesn't see it as her sons place ..seeing as he moved in with you.
You mentioned not being invited to other gatherings... some people are old fashioned and don't take non married couples as being so committed. You don't know what her view is, but it does sound like she's keeping her distance, which her prerogative. She's already seen him split from one DIL....she might be weary about getting too close to you/your kids.
He split with the mother of kids, so it would be a lot easier to split up with you.
I know my DPs felt like that when my brother got married for the second time.
I think it's important to see things from different perspectives, not just focusing on your own agenda.
Your DPs mum is really under no obligation to invite your DC, who she's seen on a couple of occasions.
Your DC have no relationship with her. There was a thread where the OPs brother uninvited her DC... I can understand why she was annoyed ... because apart from being uninvited...it was their Uncle.
A similar thread to this, had the OP begging her DH not to be the best man at his brother's wedding, because her DC weren't invited. Absolutely ridiculous and controlling IMO.
This isn't invitation by association. Far better to be dignified and when it comes down to it...the most important thing, is that your DP who lives with you, treats your DC well.
You're not in a relationship with his family and focusing on peripheral issues that don't impact on your day to day life, won't bode well for you.