Hi everyone, I'm new to this forum so i apologize if this is in the wrong place.

I've picked up electric guitar after a while and am trying to learn the Count of Tuscany by Dream theater. I am trying to play this lick at 2:27 of this video:

It is mostly "outside" alternate picking, but in two string crosses I am forced to use "inside" alternate picking. I can play the outside parts full speed without any errors, but no matter how much I grind the inside alternate picking parts with the metronome, I always trip up there when I speed it up. Having to change direction and jump over a string doesn't seem to work at high speeds .

I know that Dream Theater is not for beginners like me, but since I can play the "outside" parts decently at the same tempo as Petrucci, it is kind of frustrating to be held back by the inside picking parts which don't seem to be improving. Should I try to learn an easier song? Do I need more practice with drills? Or should I use a different type of picking? Does it just take a bunch of practice?
first off, the best edition of you playing the song will only come with practice.
Thats what you gotta do. Regardless of technique mastery, you gotta practice.

We don't know how you play, post a video or something- it is really hard to gauge what you specifically 'need' to do to improve.
"ba doo doo ba doo doo ba doo daa"
- earth,wind, and fire
When you're practicing with the metronome, work up to your "speed limit" and practice there for a minute. Then go 20-40bpm beyond your speed limit spend a short amount of time trying to make it work. It won't work, but it will give your muscles a heads up that greater speed is expected. Then spend a few minutes alternating slow and fast (the point being to compare tension/efficiency and get the fast playing as relaxed as the slow).

Also watch out for technique errors, as they will cap your speed no matter how much you practice.
When you practice, also focus on the movement of your fingers. Try to minimize movement and relax. If your fingers start to cramp, you will make mistakes that are hard to get rid of later.

As cdgraves pointed out, try to find your max speed. Tom Hess for example suggests to practice any lick at 65% percent of your max speed first, then slowly increase to 85%, then to 95%. After a few weeks you can measure your max speed again and repeat the whole procedure.
Fretello - Amplify your Skills
The Smarter Way to Practice Guitar