SIL spent the first few years of her DS's life living with MIL, and now MIL looks after him a few days a week while she works (she has moved out now). They are very close and MIL goes to his school plays, fetes etc. This doesn't bother me or DH as we tend to do these things and just give an open invitation to both grandparents if theyd like to come.
MIL doesn't see a lot of our two DC as between her work, new partner and having DN she is quite busy, but once a month or couple of months she will 'pop' in and see them for lunch or dinner.
These times she spend the whole time talking about DN. My DD will say nanny can you read me this book and she will say oh I like this DN has this its his favourite. TV shows come on and she will say oh this is DNs favourite programme do you like this too? Etc etc. Barely an hour passes before is brought up and when the DC are playing she will go on and on about her DD's troubles with DN at school or similar.
It drives me nuts!!