This isn't a matchup thread.: How do you get in and separate them? That's a tough part of this MU...
: What do you mean by "limiting Ice Climbers' movement"? Yeah, the grab is the best separation tool, but as you said, it's very risky, so when do we have to use it? I usually try a grab after a Razor Leaf, but if it misses, I'm dead... They'll get in pretty quick, so I don't know what should I do to separate them when they get close and I can't retreat...
: They'll not approach and throw IBs at you, if you FT them, it'll be stale + you'll eventually get fatigued... If the FT get read they'll roll behind and grab. And you're not gonna rack up many damage with it if they don't dash towards it or something... :/
That said, Squirtle's poking is limited to tilts and the occasional B-Air or Jab. You need the grab until middling percents, unless the Ice Climbers player starts using Blizzard, which you can stop with Water Gun (it pushes them back a great deal if they're not able to run against it).
Ivysaur's shorthop B-Air covers a large space around you. You want that space to be no-man's-land; they should not feel comfortable being there, but they have to be there in order to get their grab on you. B-Air has the advantage of not being grabbed if they shield it, which is why it's your go-to option. Otherwise, use multi-hit moves to throw them off in general (shield-grabbing as ICs doesn't work so well when both Ice Climbers have to shield multiple hits from D-Tilt, B-Air, or F-Tilt). Dash Attack works alright at mid percents to get them in the air if you expect them to spotdodge, but is risky. Either way, the most important part for Ivysaur is not to separate them; it's to keep them at bay, which Ivysaur can do while preventing the opponent from camping (as Razor Leaf beats their camping).
Who cares if you get fatigued? You don't win this matchup as Charizard by killing them off the top or anything. You separate them and then F-Air or D-Air Nana off-stage, or, alternatively, maximize damage with shorthop Rock Smash so all the shards hit. Fatigued or not, they'll do their job. They aren't able to roll through Flamethrower unless it's spaced very poorly; you're not trying to get close with it, you're trying to prevent them from being able to get through. Aim to hit the far part of it.
For Ivysaur and Charizard, most of the match is a battle of attrition. Stop thinking in terms of racking up damage quickly and ways to separate them easily, as the opportunities are usually few and far between. What you want to do is keep them out long enough where your pokes get their damage high enough to be able to separate them with weak moves that don't require much commitment. That's when you go in for the KO on Nana.