I would almost bet your mare dislikes men because she was prolly abused at a young age by men. I have a 30 year old Appaloosa mare we got dirt cheap because the university farm men tried to force load her in a trailer and she won.
My dad could never do a thing with her but I can crawl underneath her ride without a bridle, bit, halter and she will do whatever i ask her to do. My DH cannot ride her at all, she will tollerate ground work but nothing else.
My suggestion is use your new horse to pony your other one around with a saddle on it etc. get her used to your voice above her head and you touching her neck and head while riding. I always mess with mine while riding, head neck legs, flank, tail, etc
main thing is don't rush it. look into Parelli training, it is basics of trust and play and enjoying each other. Basic common sense things we forget...thinking like a horse would think.
Congratulations and good luck with your mare too!