Righto. Sorry but as soon as I read "bikini" and "HIIT" all the time I knew your wife was pissing into the wind.
I have programs specifically for female body builders I am happy to send you. One of which is John Meadows who is pretty much a legend in terms of body building.
You wife is not going to get what she needs from a PT, body building, whether classic, bikini, physique, whatever, is absolutely beyond your average PT because you HAVE to take hormone balances into account with both eating and exercise. The issue with Bikini these days is any woman can starve herself, but then it becomes a negative cycle of rebounding and back, rebounding and back.
Ultimately though, a caloric deficit is required, 100%, but until you work out your TDEE (which can be done online for free) then anything beyond that is guess work. Again your average every day PT does a 3 month certificate to help fat people lose weight. Physique building is a totally different ball game.
How you help her? Get in the gym with her, even if its to spot her a couple of times a week. Help her meal prep, but also just be understanding that its brutal. Sleep and food are easily the most important factors in the equation. If she isn't resting her body enough then it cannot recover properly so each day gets worse.
My personal suggestion would be doing strength work, carb cycle. On Cardio days, low carb, high protein. Normal days just average. Leg days up the carbs considerably.
Caveat : This is all entirely subjective also, every single individual is different and responds differently. She really needs to invest in a proper coach. Not a PT because there is significant long term risk to female fertility if rebounding/starving over a long period of time, and I can tell you from personal experience a woman dealing with infertility is a different beast altogether, and not in a good way.