I agree with this - it’s all being conflated and the @ayloanneeds to see the wood for the trees.
MIL can have any relationship she likes with the ex and her dog. OP needs to let that lie. Seemingly OP or her DH have not even met the dog in 5 years and the dog and ex live in another continent and time zone.
@ayloanis a people pleaser and bent over backwards to develop a relationship with her MIL before pregnancy shifted the dynamics. Maybe MIL was miffed she wouldn’t get full attention, maybe OP recognised her finite emotional energy needed to focused elsewhere. This is understandable but maybe the MIL sensed this withdrawal and was confused and upset. That doesn’t mean OP was wrong - just that both can be happening at once and the skill in life is emotional adjustment to shifting changes in life.
From a distance the comments from the MIL in the early days that OP has spent more time with them in 2 months than ex did in 10 years is revealing. OP look this as flattery and a delicious snub to the ex. However it might reveal that ex worked out the needy/dysfunctional MIL early doors and put in healthy boundaries or that MIL worked out OPs needy people pleasing flaw and was suggesting she was engulfing or wanted to exploit that. Could be all of it.
OP is now understandably hurt and confused that MIL is not interested in being a grandmother -possibly to OPs preconceived expectations and she reads this and her actions as passive aggressive and these are impacting her and her marriage.
The OP can choose to accept that her MIL has these priorities but she can also choose her own agency in taking responsibility for emotionally protecting herself so that she doesn’t get hurt, or it is processed quickly - and she can focus her finite headspace and energy on intentionally positive emotions for the benefit of her baby, herself and her marriage.
Seems to me OP has poor boundaries - even in her own head - to conflate a dog on another continent being responsible for her marriage disintegrating.
Start by accepting MIL doesn’t like you, never will and is hurting you. That takes time to come to terms with - but don’t get stuck ruminating there - you now have to actively take responsibility for taking yourself out of punching distance. You can do this by limiting contact, information, bland responses etc. Dropping the rope to her game without drama. Emotionally detach in your head - not to bitterness but indifference. You won’t notice her if your life is busy and fulfilling - make it so.
Then turn your back and focus hard on building an emotionally positive and stable family unit. Have you recently had your baby - could PND be in the picture as well ? It lasts for 2 years. Maybe you need some professional support at this time as well.