Potty training...the sequel!!!

So at the ripe old age of 3 1/2, Rhiannon has finally decided that she is ready to get potty trained!!! For the last week, she has been peeing in her potty regularly during the day, and as of yesterday she is in "big girl underwear" for the daytime! I'm so proud of my little one, it's been a long time coming! Of course we are having little accidents still, as I'm typing, her block bucket is being disinfected after she decided it made a good potty, but hey life's good!

Potty training - do I have a problem?

Hey ladies, just wanted to put this one out there & see if anyone has had a similar experience,or any advice!

My daughter is coming up to 3 1/2 years old, & is not fully potty trained as yet. She will sometimes pee in the potty or in the bathoom, when I take her there, and is in pull-ups during the day & a regular diaper at night. The baby books seem to suggest that she "should" be clean by now, but she doesn't always seem to beware of the need to pee, until after the event....she'll tell me when she has peed, rather than she needs to pee. I am worried about trying to force her before she is ready, & making it traumatic for everyone concerned. I have friends who have basically put their kids in regular underwear & let them have accidents until they are clean, but I also have a 15 month old son, who I can just see following us around & putting his hands in pee puddles while I'm attempting cleanup! Is she just a late bloomer in this department, should I be concerned...or am I just missing something? Arrggghh! It's not as if I want her to be trained by this time next week, but I would like her to go to preschool / playgroup in the fall & she would need to be potty trained to attend them apparently.