Squeezing when you're bottoming clenches your external sphincter, which really isn't as tight as you'd think given the amount of effort involved. I can only grip like that for a few seconds at a time.
OTOH pushing out, or bearing down, does a couple of things:
First, when initially being penetrated, it moves your rectum down a little lower in your pelvis, which opens up the anus and does allow easier initial penetration. It also relaxes the inner and outer sphincter a bit, that's why pushing helps you take a dump.
Second, it also provides a deep squeezing, which increases pressure from a couple of inches in all the way up the rectum until you hit the sigmoid colon. Once your top is thrusting away, bearing down can really increase sensations for the both of you. He'll feel like he's fucking a virgin ass and your deep nerves and prostate will get the massage of their life.
As for the second hole, yeah, it's there and fucking a guy who is big enough to get past it is incredible. You both need to be patient and slowly work it - unless you're an experienced bottom you might find that getting on top and you controlling the rate and depth is essential to working past that obstruction. Mine is about 7-8 inches in, and once it loosens and straightens out a bit and that head plows past, we're talking fireworks, man.
Best bet, unless you have a very patient, and well endowed lover, is to experiment on yourself with some larger toys. Relaxation is the key. I use a Sean Michaels dildo and find that I had to trim off the balls to get another 2+ inches in me. Now I keep my ass ready for the really big boys with a few hard workouts per week. Yeah, boy, you better deep douche that manhole.