Hi H.!
First of all I want to let you know that you're a great mother. I'm sure everyone has told you that babies don't come with instructions, so you're going to have to do what comes naturally to you.
Have a chat with your pediatrician. I'm sure she'll tell you that babies just cry when they're sleepy. It's not because they feel abandoned or because there is something you're not doing for them. When they feel tired they feel that something is "off" and they don't feel normal so they cry. Honestly crying to a baby is like barking to a dog. It's just what they do. It doesn't have to be because something is wrong or right, it's just all they know how to do so they do it. My little guy is 7 months old now and the happiest baby I've ever been around. He giggles and coos and chatters all day and is very giving with his smiles. BUT, every night when I lay him down to bed, he screams his head off anywhere from 5-15 minutes. He always has. I do have a 10 minute rule where if he cries flat out for 10 whole minutes I will go and interact with him (pat his back, turn on the glo-worm, hum a little song to him) but I don't pick him up out of the bed. When he wakes up in the morning or in the night, he's just fine.
In regards to the other's thinking your girls are just going to want their mom all of the time. Well DUH! Of course they're going to want to have you all of the time. Whether or not you put them to sleep won't have any effect on that. The issue you may run into, however, is that they could find it hard to get to sleep without you doing your "magic sleep mojo" on them when you put them to sleep. Perhaps you could develop a bedtime routine that you do with them each night rather than rocking them or walking the floor or whatever it is you do to get them to sleep now. Each night we go for a jog then he gets a bath then eats solids then nurses while I read a story then he goes to bed. We do it every night and it works for us. I mean, Oliver still cries every time I put him in bed, but it's a lot less than when we started the routine in May.
I think it's important that you get your boyfriend on your side. That might require some give and take. You could try it his way and let him put them to bed while you do something else during that time for a week. Who knows, it could work, but he should be prepared to do it your way if his way doesn't work. I have no advice for the in-law situation. Mine live in an entirely different country. My mother lives 5 hours away so when she sticks her beak in I just thank her for the advice and tell her what I'm going to do. If those two things happen to be the same thing, yay. If not, she must just deal with it. :-D
Best of luck and let us know what you decide to do!