I can't promise it will help, but I do know that people who turned on advanced rendering did have more success with pet-fluff. However since it adds a lot of graphics to the game there's a chance it will slow your game down or even crash it. Be prepared and save often until you figure out how much your laptop will handle!
Your story sounds similar to mine. I had a desktop that was so old (well it was the first windows to run Vista) and it had no graphics card... when I was using that computer was before my boyfriend even taught me about ram and my graphics card... I thought Sims would work on EVERY computer. When I got my laptop I was disappointed because while it had better ram and a so-called "graphics" card it was all integrated and very poor quality. I finally took a lot of my saved money and bought a brand new computer from HP that I designed myself to ensure it worked perfectly with Sims (yes, I bought/built a new computer just for Sims, I'm that crazy). If the funds aren't there though (and I definitely know that feeling) then I recommend looking at small fixes like advanced rendering on, everything else low.