Personal trainer to help with strength?

Unless you are injury prone or have some type of functional weakness I think coaching would be a better investment than a personal trainer that doesn't really focus on triathlon training. Since you mentioned working on form, a swimming coach could be very helpful. Masters swim coaches can be a huge improvement.

If you want some guidance on strength training, I'd advise just signing up for a session or two so he/she can show you how to safely use the equipment and do exercises--no need for an extended commitment. Most tri-related strength work can be done with pretty basic bodyweight exercises, unless you have specific injury-related concerns.

I'd caution working with a pure trainer.

As a coach, the strength routines I send my athletes are very specific to functional fitness, core and stability. They end goal is to be a better endurance athlete. Some trainers might be good, but the bulk I have seen barely have enough knowledge for regular strength work and very few have an eye for what an endurance athlete needs.

If they start sending you to the squat rack, bench press and other major weight moves for every workout, its not going to benefit your endurance life as well.

Not saying all trainers are crap, but what I have seen personally does not install me with a lot of confidence.

What I have done is get recommendations for what exercise to do rom my tri coach, then use videos she sends me and/or ask trainers at the gym for advice about proper form if I'm unsure. In once case there were quite a few free weight and machine exercises I was unfamiliar with; since my coach was half a world away I scheduled a session with a trainer at the gym (a cyclist friend recommended him) to show me the correct form for the exercises I had been given. I probably wouldn't trust a trainer with recommending specific exercises, unless he/she had tri coaching experience, nor would I spend the $ to work with him/her on a regular basis.

I worked with a trainer for about 6 months a few years ago. He was a crit racer and had dabbled in triathlon, so he really knew how to get me working the right way. Ultimately he decided to go to graduate school, and none of the other trainers at the gym seemed like a good fit, so I've never worked with a trainer again. I have never been as good shape as I was then. My cycling was stronger.

I worked out with a trainer for three or four years while I was fully engaged in triathlon. I can't say the strength exercises were specific to tri but I did deliberately stay away from leg weights. A kinesiologist I know who had been a pro cyclist told me triathletes train themselves to do one thing very well: move forward. So when someone goes to a physical therapist for knee/shoulder issues related to running or swimming, what's the first thing the therapist gets the patient to work on? Building functional strength to reduce muscle imbalances. Strength work represents the ounce of prevention that wards off all sorts of problems.

As to whether you need a trainer, all I can say is, form is everything. If you don't have a background with strength, it would definitely be worth a few sessions with a trainer to make sure you're doing it right. As for myself, in a hundred years I was never going to push myself as hard as the trainer got me to. Totally worth it.