I have been in a similar situation, although the person that mil was running down was me. DS was also 2 although very verbally advanced for his age. I was in hospital for 6 weeks at the time- on bed rest as I had gone into premature labour with dd and despite managing to stop labour, contractions started whenever I mobilised.
My ds came in to visit most days and dh had been staying at his dp’s whilst I was in hospital. Dh was being very cold and cruel to me at the time, he would dump ds with me and disappear to the cafe. As soon as dh left the room my ds would say ‘my Nana not like you Mammy.’ ‘Nana shout at Daddy, she not like you Mammy’. Ds is autistic and was very much a parrot, anything that was said around him would be repeated back. He wasn’t imaginative, he would purely repeat back what had been said to him. DH was aware of this as ds had repeated back to me his Daddy using language that was rather colourful whilst driving!
After two weeks of hearing ds repeat awful things that mil had been saying about me and my Mother, I lost it with dh and asked him wth was going on at his Mothers and told him everything that ds had been telling me. DH admitted that everything ds had said had happened, mil and FIL were having huge arguments with dh, demanding that he leave me and take custody of ds. Apparently I could have dd, as dh didn’t have a bond with her yet, due to her not being born yet. (In-laws had previously flipped the lid when dh proposed, he was thrown out and basically disowned as they felt I was not good enough for their ds. I offered to let them back into our lives after we were married and I fell pregnant with ds) I flipped and dh took ds to stay with my dp’s.
In my experience, as a Mother you know your dc! If your dd is prone to making things up, then obviously you would take what she said with a pinch of salt. However, given the change in behaviour and your dd commenting that your MIL had said something about your DM, what your dd is saying, explains the change in behaviour. So I would be discussing seriously with my dh why this needs to stop!
For a start, if mil dislikes her house in America she can bloody sell it! It is outrageous to demand to stay with you for 6 months of the year! I would be putting my foot down and saying short visits are welcome, anything longer and she is outstaying her welcome. I would also be making sure that you don’t leave your dd alone with your mil. Your mil is clearly manipulative and an unhealthy influence on your dd. So unfortunately you will need to make sure that you are with your dd when your mil is around.
If your mil provides childcare whilst you work then I’m sorry but I would be finding alternative childcare! I would also make sure that your dh tells his dm that you both know that she has been running your DM down and that it needs to stop.
Unfortunately, it sounds like your dh is reluctant to believe your dd, so likely will do none of the above. In that case I would be sure to let slip to mil
‘you need to watch everything you say with dd, she is a little parrot who repeats back to me everything she hears! She got DH in trouble the other day for saying bad words in front of her. You should hear what she has said you have been saying! There are no secrets in this house when dd is around’
In my situation, dh was being heavily manipulated by his dp. Thankfully he finally grew a backbone and we have been nc for seven years!