What a lucky MIL you have afar - I feel she should appreciate the amount of time she gets with your little one, especially if, as you say, she babysits more than anyone else - there are hundreds of grandmothers on this site who never ever see their grandchildren for various reasons - distance, feuds or whatever.
Could your husband have a word with her?
It sounds like you are a great little family and you must never stop enjoying family time together - that is so precious.
Perhaps if your husband has a quiet word, explaining that you both appreciate how much she loves your little boy and how excited she is about her first grandchild. Tell her she will always be special but that she needs to share him with others who love him - your little boy will be taught he has to share so why shouldn't she?
Perhaps if your husband is reluctant to do this with his mother (most men are!) does he have a sister or aunt who may be able to help?
If they get along could your mother have a chat? She knows the joy a first grandchild brings and could possibly empathise but get your message across? Perhaps they could take him out together and use that time to broach the subject? Presumably there was 'the other grandmother' to consider when your mother's other grandchildren were born?
Does MIL get on ok with you apart from this, or is there also an element of 'this woman took my boy off me and now is keeping my grandson away from me'?
If so, she may need a firmer approach but try the softly softly approach first as it would be so sad for this to turn into a major rift.
Keep in touch with us here - I am sure you will get other suggestions!
Good luck my love, you are obviously a very caring DIL