outside unit not coming on

Hi, I have a heat pump that is not cooling. I checked the compressor and refrigeration line and they are good. I opened the air handler and the coils in there are getting cold too. When I turn the unit on to cool I realized that the heating elements are getting turned on as well. This heat is negating the cold air. I disconnected the heating elements and the temp dropped from 88 degrees to 76 degrees overnight. The thermostat was replaced last year so I do not think that this is the problem. I thought that it could be the heat sequencer sticking open ? The sequencer has 15s2 H24V 309562 printed on top. I went to Grainger and they have a replacement but I need to figure out the delay times to get the right replacement. Before I proceed I wanted to see if I could get some advise as to if I am on the right track or not. Thanks in advance.

Our house is a one story 3 bedroom, 1 bath, hallway, kitchen, living room and Dining room. For the life of me I cannot figure out why I can't keep the living room, dining room and kitchen as cool as the other rooms. I am a very hot natured person and can tell even the slightest of differences when it comes to being cool. It's an old house, no ceiling fans either. The vents closest to the outside heat pump are 2 bedrooms, a hallway and a bathroom which stay cool. The other bedroom stays fairly cool but LR, DR AND Kitchen do not. I will state that in the kitchen we have 1 fridge running, a deep freezer, and a utility light that sits above the cabinet. In the dining room we have a computer, another fridge and a floor fan running. In the living room we have a small Stanley utility fan, a 48" projection TV, a ps3, a lamp. Aside from all that running, those three rooms are also connected together. A back door in the kitchen that is used quite often and a door in the dining room that is used even more often. Six people live here and all of us stay usually in the living room/dining room area. The unit we have is 13 years old, but has been serviced this year and seems to be running great. 12 seer 2 and a half ton Heat Pump full with freon. Our house faces north with the heat pump being on the east side of the house where the coolest bedrooms are. The hottest rooms are on the west side of the house. Each room has 1 vent in it. The rooms closest to the unit stay pleasant even when the unit shuts off, but the kitchen, living room and dining room are very stuffy when the unit knocks off even with the above mentioned fans running. What could be the problem? Could it just be all the stuff we have running? People notice it besides me. And I just don't know what can be done. Unless that heat pump is constantly running those three rooms are beginning to be a nuisance to even be in. One floor return sits in the middle of the dining room/living room while the other is in the hallway. Both have brand new filters as well. Please give me some tips to try and keep these rooms cooler. Should I turnoff the fans? Is that causing a problem? I realize the air has to travel further to these rooms through the ducts and could become warmer. The ductwork is underneath the house in a crawlspace which seems pretty cool. And to be honest the crawlspace would probably be cooler than the three rooms should I go under there. I would like to add that since the 3 hottest rooms are on the west side it seems there should be more vents for that area since that's where the sun hits the most. There are 3 total, one in dining room, 1 in living room and 1 in kitchen. The room size of all three is about 50 length 35 width HELP HELP HELP!!!!!!