Best Core Stability Exercises for Lower Back Protection

I have had a history of lower back tweaks during squats and I have realized that my core stability is just not where it needs to be. I am not talking about six pack abs I am talking about the deep internal stabilizers. I live in Ottawa and I am looking for a solid routine I can do at home.

I have been doing planks and deadbugs but they feel a bit too easy now. What are some more advanced core stability exercises that actually carry over to a heavy squat? I have heard that Suitcase Carries and Stir the Pot are very effective for this.

Do you guys do your core work at the beginning or the end of your workout? I have heard conflicting advice on this. Some say it is better to pre-activate the core while others say you should not fatigue it before heavy lifting. I would love to hear what has worked for you.