It gets easier over time, but I had to first break everything down into simple 1x measure phrases: a bass line in the LH OR a riff in the RH. Then I'd practice both hands together round the circle (I'll call hands together a 1x measure groove).
If that's still tough, you might have to go one step simpler and run basic triads and inversions around the circle, then move on to 4-note chords. After that, the 1x measure riffs will be an easier step.
After awhile, it becomes easier and you'll pick up the basic LH/RH "grooves" almost immediately, even if it's more than 1x measure.
An excellent goal is to eventually be able to run the phrases "round the circle" in a 4-5-1 progression. That's a nice level to reach and is a great place to really feel like you're playing with the music.
NOTES:
There are different ways to practice all the keys.
1. Round the Circle of 5ths (or 4ths)
2. Chromatically
3. If you're already doing 4-5-1 progressions you can use the 3x diminished scales as a cheat/shortcut to "play in all keys". You only have to practice a 4-5-1 progression over one of the diminished scales - to hit all 12 keys. Though you should rotate the diminished scales on different days just to get the full benefit and still take advantage of the cheat/shortcut.
The 3x Diminished Scales:
C = E♭ = G♭ = A
D♭ = E = G = B♭
D = F = A♭ = B
PRACTICE REPS
Personally I visit each phrase for at least 7 practice sessions. If anything takes longer than 3 minutes to run through "all keys", it's too difficult for me and I make it simpler before continuing. In the beginning I could only do very simple phrases, but overtime my skill built up so even complicated 4-5-1 musical phrases can be run in all keys in under 3 minutes.
For important phrases, I extend the practice session by 7 days at a time, that way easier phrases can be retired at 14, 21 or 28 sessions. I've never had to practice anything beyond 28 practice sessions - that seems to be the point where even the most difficult phrases get demolished and become "fluent".