J.S.
Toddlers become very attached to the objects they are holding. Not so much in a security way, but they feel as if that toy in their grasp is an extension of their own self. When another child toddles by and yanks that toy out of their hand, she will feel, literally, as if she's been amputated. So it's important to understand how your child feels when this sort of thing happens during play. And, that's why development psychologists recommend teaching our children to "trade" instead of "share". With sharing, the process involves giving away a toy with the hope that it will come back. This is too much for young toddlers to process. With a trade, there is always an object for every child to hold and connect with. That's why distraction works sometimes. Rather than wait for playtime to turn into taking away behaviors that you then have to manage, try to get your older toddler to practice giving. Ask your 3-year old, "Can you find a toy to give to baby? Baby needs to hold a toy." I realize that your 18-month olds are toddlers and not babies but establishing more giving dialogue and behaviors might help.
Secondly, understand that as much as we want our little angels to be loving and sensitive to all living creatures on earth, the reality is that young toddlers can't differentiate between object and people having feelings. When we see our 18-month old knock down another child to get to a toy, we think that is rude and rough play. Actually, the toddler only perceives the other child as an object in her way of getting to a toy she really wants. They don't comprehend that there are feelings involved. So we need to teach our toddlers that there is a difference between people and toys. We say, "You have to go around (child's name) to get the car. Go like this," and then physically help your child find a path around another child to get to the toys. And you can start introduce feelings by teaching, "It makes (child's name) sad when you take a toy from her hand. Let's find you a good toy right now so (child's name) can be happy with that toy and you can be happy with that toy."
It takes a lot of patience and perhaps a new way of parenting your children while they play but you are a loving mom and I know you can do it!