A. First, a few questions: Does your mother have a regular babysitting gig with your brother? Do both of you live close to her? And just how old is Grandma?
Why this inquisition? Because I'm trying to take the emotional aspect out of the situation ("Mother always did like him best!") so that you can figure out how to get the help you need.
Let's assume that your mother does not have a set babysitting schedule with your brother's family. The fact remains that after more than two years, he and your sister-in-law are used to having Grandma on call, and she's used to wearing a beeper. And that may be why, when you summon her, she in effect answers, "Not my station." I'm not saying that your brother should have dibs on your mom's time because of some "first come, first served" rule. But you should try to understand that routines have developed. Also understand that while Grandma may really want to help you out, she probably just doesn't have the energy to be everyone's safety net.
Okay. Now that we've established that neither your mom nor your brother is being unfair (just for the sake of argument), try to pinpoint what you need. Is it full-time babysitting when you go back to work? A few hours a week so that you can run errands or make dinner with two hands? Or are you simply looking for some company now and again? After assessing what you want from your mom, go ahead and ask. If your brother has lined her up to babysit on certain days, ask if it's possible to trade off one day. If your mom just stops over at your brother's, ask if she'll consider breaking that habit and coming by your place once in a while.
Just as your mom had plenty of love to give both of you, she has plenty of love to give two grandchildren. You simply have to be specific about when and how often she doles it out. After you and your brother hash this out, there are only two other things to do: Look into finding a reliable sitter to be a mother's (and brother's) helper. And take Mom out to dinner. She deserves it!