Two years before spaying? Yikes...that is pretty uninformed advice. I would consult with a knowledgeable vet in your area. Better yet, get on some websites of local area rescues, where you are more likely to find a plethora of information on that topic alone.

As to your timid female, I would say you need to be more patient. I know how hard it is. If you search on here for my posts on Minnie, you will see I am going on THREE YEARS! I cried the first time Minnie came out with me even in shouting distance. The first time she purred when I pet her? Oh, it was like Heaven on earth. I still can't approach Minnie, but, at least she doesn't always run everytime I come within 5 feet of her.

I don't suggest forcing her in any way. The idea of reading aloud, while sitting near her, leaving treats near her, avoiding direct eye contact, and never, never making her feel cornered by you can help. It just takes alot of time. Since you have another cat, be sure to make a big fuss over him/her where the timid female can see it. She needs to associate you with all things loving.

Don't give up. Be patient, and know that it is possible she won't be the lap cat you had hoped for.

Good luck.