I'm assuming that what you mean by position chart is just a letter name to position number reference. That's not going to be enough—when you open a valve on the trombone, all of the positions get larger: you can only fit 6 positions on the slide with the F valve down, and only five with both F and D. I'm going to provide you with the following chart, showing the approximate slide position adjustments made when using a slide trombone with valves.
Bringing the slide into the proper position will make it easier to play these notes in tune.
As far as actuating the valves themselves, no one will disagree with you that the bass trombone with traditional trigger placement is an awkward instrument to hold. (Even just from the sheer weight of it.) Many bass trombonists use an accessory to help support the instrument with more than just the two little fingers on your left hand. There are TONS of accessories out there, but some of the more popular ones are the Yamaha Trombone Hand Strap (very inexpensive) and the Edwards Bullet Brace.
These may help, but if you're not holding the trombone properly to begin with, they will probably not do much good. If you are using a traditional grip, make sure you are supporting the weight of the instrument with your pinky and ring finger wrapped around the bottom slide tube. The thumb and middle finger should be free to actuate the valves. (Try not to rest too much weight on the thumb with the trigger bar.)
Developing the bass trombone technique will depend greatly on whether your F and D valves are dependent or independent. Dependent valves are stacked so that actuating the D trigger will do nothing unless the F trigger is already open. Independent valves are stacked along the slide receiver tube so that the D trigger can be activated by itself. All of these valve combinations give you MANY alternate slide positions in the mid-low register. Professional bass trombonists utilize these alternate positions and valve combinations in order to minimize slide movement and increase flexibility.
In order to develop this technique, you will need to do a lot of experimentation to find the exact positions for the correct tuning on your particular instrument. When you open a valve, you change the harmonic series you're playing in from B♭ to F, D, or G. The chart above gives you some of the notes possible with both the F and D triggers active, but here's a more complete/concise example:
Note where the overlaps and breaks occur in each of the series of slide positions for each valve combination. Trombonists often forget about the third partial of the trigger combinations, but this can simply a lot of technical passages with regard to slide movement.
If you have a dependent valve section, this chart is going to be pretty accurate. However, if you have an independent valve section, it is likely not going to be exact. There exist MANY alternate tunings for the independent second trigger—if the 2nd trigger side alone does get you the G harmonic series, then likely the F/D combination is going to be closer to an E♭ than a D. (Conversely, if the F/D combination gets you an in-tune D, the 2nd trigger alone will be closer to G♭.)
All it really comes down to is that you've got to experiment with your own instrument to identify what's possible and where on the slide the notes are going to be in tune. If this is all largely over your head, you should focus mostly on becoming familiar with low D♭2, C2, and B♮1 as double-trigger notes. The Tyrell 40 Advanced Studies for B♭ Bass is an excellent etude book for developing technique in the double trigger range of the bass trombone.
I hope this answers your question. If it does not, please elaborate in your original post or in the comments.