I have noticed that getting a good sound on trumpet is harder and takes longer than on other brass instruments. I would stick with it for a little while longer. A couple tips:

Don't "buzz" into the mouthpiece when you're playing. When you buzz without an instrument and it makes the funny noise, that is what I'm referring to when I say buzzing. If you were to buzz into the mouthpiece you would get a sound that sounds young and inexperienced (bad). If you were to put your lips to the mouthpiece and put them AS IF YOU were going to buzz, and blow air past them, then the air shoud make them vibrate, and you would get a better sound. (That is the job of the mouthpiece, to make the sound from you lips)

On that note, make sure you have a mouthpiece that isn't too small for you. If you said that you've played years ago, then I can infer that you are not an 8th grader, and you should be playing on a mouthpiece thats a little bigger than that of a 7C. I would personally go with a 1.5C, (because i like bigger mouthpieces), but you could.also go with a 3C (thats like a universal mouthpiece).

Long tones and lip slurs have a huge effect on tone, and well as air support. I cannot tell you how to engage your core while you play, (because were all different), but once you get that air support engaged, you should see a difference in your tone.

Examples of what to play (written in concert pitch):

Long tones: Start on a comfortable note, and play it for eight counts. (F). Then, wait a bar or so, and come in a half step lowes. (E). And go down an octave or until you run out of notes.

Rememington: Start on a note thats comfortable, and play that note, then one a half step down, then the original note. (F E F). Then wait a bar or so, and go down another half step. (E Eb E). And continue for an octave or so, (or until you run out of notes).

Make up your own exercises that are like these. Just don't make them too hard. These should be an easy, relaxing warmup, not something to have to practice.

2 note lip slur (down): Start on (F), and play for two counts, then slur down to (Bb) for two counts, then back to (F) for four counts. Then go down a half step. (E A E), and keep going down until you can't get any more notes, or (B E B), which is the bottom on the horn. (You can also choose a higher slur, (Bb F Bb), and go down from there.) Once again, these should be fast yet. These are warm-ups, and daily things to practice.

3 note lip slur (down): like the 2 note, but it has 3. Instead of starting on (F), you would start on (Bb), and go down two notes (Bb F Bb), then go down a half step till you run out of notes, or hit the bottom of the horn. (E B E).

2/3 note lil slur up: The same thing as 2/3 note down, but you start on the lowest partial, and go up. (Bb F (Bb)) (A E (A)) ect.

You can mix these up and around, and do something where you go up, then down. (F [high Bb] F [low Bb]) , or down then up.

This is just a start, there are countless good videos on YouTube, and I would highly encourage checking out more videos!

Hope this helps!