It is amazing how many people acknowledge that the mum will miss the baby, despite the fact that the OP knows why she is going, knows about time and how long three months is, and most of all has a fundamentally has the understanding she is coming back.
The baby has none of this. Don't you think that the baby is going to fare worse than the mum?
If dad had been primary carer from the start it would be different. It is not mum v dad. It is who is primary carer. At the moment it is mum, when mum goes it will be dad but presumably not all the time, will it be dad at night and MIL in the day? When the OP comes back will the child view the MIL more as primary carer? That would really sadden me as a mum but more to the point how confused will the child be?
It's great the mum wants to something good and fun but having kids often gets in the way of all that! It if was essential, it would be different.
OP please do your own research on this.
None of the people cheering you on will be around when you get back and find your baby is mistrustful of you. I hope it won't happen but I would be concerned it would and there is no way I would do it. My son is adopted. he had a birth family, (still does but doesn't see them), a foster family (we still see them about twice a year for his and our benefit) and his family now, our family for life. He had those changes but he was older, 3 years not ten months, and he has come through it all.
IMHO it is not worth putting very young kids through this stress if you can avoid it.
Your name is Littleworrier, is that because you rightly acknowledge this is a worry? If so, why be swayed by others who assure you all will be OK. maybe it has been for some. I don't want to challenge anyone else's experiences except to say not remembering something is not the test of whether it has affected you, especially not in children under three, and especially in pre-verbal children. Please just read up on this decide for yourself.
All the very best.