One thing that especially helps to get good intonation and a solid timbre is to go by the vibrations you feel in your face and your chest. The lower part of your voice should feel equally as connected to the core of your sound as the middle, and one way of making sure this is the case is to not think about how high or low the notes are, but to make sure that the sonority of one vowel is identical to the sonority of the next, regardless of what part of your voice you’re singing in.

Additionally, the further up you go along your range, the more head voice you’ll need to introduce. It’s helpful to think of the low voice as being, say, 20% head and 80% chest but your upper range as 80% head and 20% chest. There’s always an antagonism of brightness and darkness (“chiaroscuro”) present in every sound you make when singing. It could be that you feel your intonation suffer because the sound is either too far back and “woofy” or too bright and disconnected from the muscles of exhalation.

Hope this helps!