You must be exhausted with 2 babies keeping you up. I can understand what you are going through as I have an 8 month old teething baby and a 3 y.o. who no longer naps during the day. Also, my first child never slept through the night till after 18 months. I don't sleep much these days and I never get a chance to catch up during the day. My heart goes out to you.
Your oldest child at 22 months is still pretty much a baby and really needs your comfort. I'm not a fan of the "cry it out" method because it ignores the need that the child is expressing for security and reassurance. It also increases the stress hormone, cortisol, in the body which could lead to health problems. We tried to let our first child "cry it out" and it was a disaster. She would cry till she threw up and then after we changed her bed, she was inconsolable for a very long time. I changed my ways and just comforted her when she needed it, rocked her to sleep before bed and tried to hold her more throughout the day and sometimes even slept on a foam mat on the floor beside her bed just to get some sleep. Eventually her sleep habits improved. Now she's a terrific sleeper. Goes to bed at 8:30 pm and sleeps till 7 a.m. She's also a very secure, confident child who shows no jealousy of her baby brother.
You have your hands full, but keep in mind that this is just a stage. Some day when your babies are bigger, your house will sleep. Right now they both just need so much from you and your husband. Parenting is a 24 hour job rather than a 7a.m. to 7 p.m. responsibility. I recommend checking out from a library Dr. Sears' The Baby Sleep Book (it also talks about toddlers/preschoolers sleep problems). It helped me a lot. Now I don't feel so resentful when my kids rob me of sleep since I understand the physiological reasons behind their sleep disturbances. Best wishes! R., married certified nurse midwife mom of 2. SAHM since 2005 and loving it!