Why are you feeding baby twice before bed?
My advice for your baby: Don't do the 4pm bottle. Breast feed then, and then do the bottle at 8pm. Breastmilk is digested VERY quickly, so put off feeding the peas until 8:00. Feed him all at once and then spike an 8oz bottle with breast milk and a good portion of rice cereal (don't forget to use a nipple with a bigger hole or he will get frustrated trying to get it out...and you want him to get it ALL out). If he isn't downing 8oz at a feeding, you need to move up a nipple size. After dinner, start a bedtime routine...a nice bath with the night-time wash. Keep it quiet and calm. A gentle massage with warm baby lotion, soft songs, then PJs and go sit in your customary breastfeeding spot for a little mommy/baby time. This is not supposed to be a full feeding...just enough to "top him off" and make him super sleepy. Then, just before he's fallen asleep, put him in bed (don't let him fall asleep at the breast...you want him to fall asleep on his own). If he's already pretty much asleep, don't use any of the machines or toys. If you are worried about something waking him up, use a purly white noise...like a fan. Try to use as little light as possible in his room...remember, humans are wired to wake up with the light. Kids are only afraid of the dark if they are taught to be (both of my boys have slept in a pitch black room for their entire lives with no problems).
If he wakes up, and at least 3-4 hours have not passed, don't feed him. He doesn't need to eat. DO NOT turn on a light, and avoid picking him up. Check his diaper, make sure the temperature is comfy, snuggle him back in with his stuffed toy, and let him be. Don't swaddle him...and if he is rolling over, go ahead and let him sleep on his tummy (which is what helped both my boys fall asleep very easily). Don't start up any toys or machines or lights. White noise, but no music. You want him to stay in that "twilight" of sleepytime. If the TV is blaring in the next room, turn it down when you open his door. Avoid anything that is going to startle him into being fully awake.
For your daughter: You have too much stimulation going on. Cut it down to one book, NO LIGHTS or toys in bed, you should not by lying down with her. All toys should be put away. With my boys, we read a book downstairs after PJs are on and teeth brushed. Then go upstairs and do the same routine every night: I turn off the light in their room, and turn on the hallway light. Then I put them both in their beds. We then each tell eachother one good thing and one bad thing during our day, and tell eachother what we can do to make tomorrow better (for little ones, you can help her out a bit). Lastly, I sing their song ("Dreamland" by Mary Chapin Carpenter), give kisses and hugs, and leave. I shut off the hallway light and that's it.
The gate was used when they'd get up and come out...but isn't necessary any more. When they'd get out of bed, if they were really noisy, I would just go in and put them back. No talking, just back into bed. If they were quiet, I'd just ignore them. Eventually they get back into bed or fall asleep on the floor (and I put them back into bed). Often, the attention you are giving can be a problem. Unless she is being obnoxiously loud, or playing with noisy toys, ignore her. She's winding down in her own way. But once it's about 30 minutes after bedtime, all toys should be taken away...because that's what is keeping her up.
Good luck!