XP Home doesn't allow you to remote desktop into it. You need XP Pro in order to do that. Also, when you RDP (remote desktop) into an XP/Terminal Services box, the current user session is ended and they are logged off (unless you're RDP'ing into a server product, which has 2 RDP + console I believe).
The best bet if your mom is using XP Home is to use the Remote Assistance wizard, which I believe also integrates into MS's Messenger chat program. This will allow your mom to invite you to share control of her system while she remains logged on. This is probably your best bet given your setup. You could also try out VNC, although Remote Assistance is probably good enough!