I'll try to get this all out in one go so apologies if its long!
Anyway, FIL wants to look after ds (20 months) one day a week, not to do anything amazing just take him to the shops or to see his aunties etc. I'm really not comfortable with it and really don't want him to but dh says i'm being very unreasonable and is trying his best to persuade me otherwise.
There are many reasons i don't want him looking after him by himself, the main one just being his behaviour when he is around him. He accidentally called himself daddy to ds last week, he completely smothers him. He comes to my house to see him and will be here for an hour and completely ignore me, honestly he won't talk to me at all he just follows my ds around (which annoys him tbh) The man has very poor personal hygiene, my house really smells after he has been here. I've NEVER been to his house (lives alone) because my dh won't let me it is THAT bad! He has lived there 7 years and doesn't own a hoover and has never cleaned his cooker so you can imagine.
I let him take him once for an hour to go and see his auntie but i found out afterwards that he didn't change his nappy the whole time he was there and just left him to eat his lunch in a shitty nappy 
He doesn't bother with my other 2 children (both girls) to the extent when dd1 saw him without ds being there she said 'now you'll have to speak to me because ds isn't here' and she always comments on how he ignores her. Everybody has noticed it. Dd2 is only 6 weeks old but hasn't even acknowledged she is here, didn't even get us a card or anything when she was born, no congratulations and he hasn't even looked at her let alone held her. Was complete opposite when ds was born.
Anyway the main reason it bugs me is because i know he only wants to look after him to get one up on mil. They have been divorced 20 odd years and mil with new partner since then. They all seem to get along very well but their relationship is very odd. Before mat leave mil would have ds every friday and fil would just turn up and stay there all day following ds around all day! But what really got my goat was hearing an answerphone message from fil to mil saying how he had seen HIS grandson today and because ds has same surname as his that means he is HIS grandson only and not heres. It was really very nasty and really upset mil (who i love to bits). He phones me up all the time trying to catch me out on when she has got him so he can go round and pester her, last night he even made me describe where the playgroup is that we go to because he didn't believe thats where we were going and ds wasn't at mils!
Wow this is so long already and theres probably more but i can't think right now. Thanks for staying with me! Anyway i really do not want this man looking after my son on his own, he can't look after himself let alone a boisterous toddler. I just do not feel comfortable with it. Dh says i'm being a total bitch and that i should let him because he doesn't want his dad to fall out with him (everybody panders to what he wants because he gets really moody and won't talk to anyone for ages if he doesn't get his own way) and thast he feels sorry for him and i'm stopping him seeing his grandson, which i'm not he is perfectly capable of coming to mine to see him he doesn't NEED to take him out for the day.
AIBU to not let ds go with someone i don't feel comfortable with or should i just give in to dh?