Split Training Question

I have been using my home gym for over a decade. Would do 1 training session a day usually by body part. I do not have a lat pull down machine, cable machine or leg curl/ leg extension… the gym where I work has these machines. I have started using them on my lunch break and hit exercises that I can’t do at home.

For example I will do tricep push downs and extensions on the cable machine and when I get home complete my workout with biceps, close grip bench… same with lat pull downs… i have been doing weighted pull ups for a decade and it seems to fatigue my arms, forearms more than lats… i do wide grip lat pull downs at work, close grip pull downs… and when I get home do barbell rows… and t bar rows… then dead’s and hyper extensions.

Is there anything wrong with training like this ?