Kula is like K' in that she doesn't have a command grab or a whole buttload of invincible moves. You can apply frame traps and aggressive pressure on Kula that will make her a lot less dangerous because she can't move.
If Kula is doing Lay Spin at a distance, she's likely using far st.C, CD, or st.B. If you block far st.C or CD and they cancel into Lay Spin, you can't do anything. They're too far away, but you're at neutral. In fact, you're a little faster. Kula's st.B is 4F, K' d.B is 4F. If she does Lay Spin at that distance and tries to poke you with st.B, you beat her out with d.B. This proves she is negative on block still. Anything she does after this blockstring will not beat you. Throw out a d.B to keep her honest. If she starts to jump after Lay spin to avoid punishment, you can anti-air her normally.
If she does st.B, that's not even a block string. You can DP her after she does st.B and cancels. She has to space it far enough and that's probably gonna be after some d.Bs. It's not easy to buffer a DP after one st.B, but with practice, you can. However, after two d.Bs into st.B, you can expose that weakness with dp+C real easy. Dp+A trades most of the time but allows for a follow up qcb+B.
As for when Kula stops using Lay Spin and starts using Ice Breath, here's the scoop:
Use dp+C when you think she does st.C to start into Ice Breath. It'll go right through and interrupt her before she does it.
Use qcf+BD (EX Blackout) to get around her when she does st.B into Ice Breath at max range. Other methods work, but you will trade if you don't delay it at the right moment. This is 100% insurance in that you will get a full combo punish when she does that.
Use dp+AC (EX Crowbites) when she does far st.C into Ice Breath. For some reason, K' will dp the first time through it and then rip her to shreds.
Also, qcb+BD (EX Minute Spike) works on every version. EX Minute Spike has guardpoint on the its first frame of start up. It eats up frame traps that are tight like that. You get a nice corner carry too. Try it out in training mode, tell me what you think.