My DS is 5 weeks old. MIL is lovely but can be overbearing. Before DS was born she acted like he was hers, referring to him as "her" baby on Facebook, making 'jokes' about how she will be the favourite nana etc. I was dreading giving birth, having visions of her snatching him off me etc but she was actually okay. She did ask if she could babysit him for a few hours on the following thursday after he was born as we left the hospital but said it was fine if i didnt feel ready and mentioned that she didnt let her DH take her babies out for the first 6 months 
It feels like she only wants to see DS if she can take him out and show him off, she never comes to our house to see him. Reluctantly, Ive let her take him out for an hour or two when he was 4 days old then again at 3 weeks old. She told my DP she feels she doesnt have enough alone time with DS last week. Wtf? he is 5 weeks old!
Anyway, when she took him to a cafe my friend works at. My friend told me today she saw MIL, who was telling some elderly ladies that my son was hers!! Now, she could have been joking but my friend overheard her describing her labour and birth with him. This has really creeped me out
DP insists she was most likely joking but with her other behaviour/comments I feel really uncomfortable letting her take him out again. Whenever I say no to her or an excuse why not she ignores me then cries to DP. I just dont know what to do!! AIBU or is she acting really odd? Or am I the one over reacting?