Hi C.,
Many 3 1/2 year olds don't nap. My daughter was done napping by her 3rd birthday. Nw, as a SAHM you may want that naptime, I worked f/t and was so glad to have our weekend afternoons for fun family outings. If she was truly tired, she would fall asleep, but it is fine to institute a quiet hour where she needs to stay in her room, look at books, listen to music, play quietly. I would not have her in her room the entire time baby brother naps. Use his nap time as time for the two of you to spend alone together doing fun things. I would cut out the actual nap, do quiet hour and put her to bed earlier. You may find that she sleeps a bit later in the morning too. I wouldn't do any bribing, I would just tell her how it is, 1-2pm is quiet hour, this is what you do during quiet hour, it's a rule and these are the consequences for breaking the rule. I wouldn't spend time with her in the middle of the night, if she gets up for the bathroom, tuck her back in, give her a kiss and be on your way. It is fine to tell your child that you have needs too, and that parents are tired people who need to sleep during the night. While I was there for my kids when they were scared, sick, infants, etc., I didn't feel a need to parent around the clock simply because they felt like being with me.
Goodluck