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Russian interest in the region can be traced to 1559 when Ivan the Terrible annexed the Caucasian city of Astrakhan, former site of the Tatar khanate. Forts were built in or near Chechnya's neighbor Daghestan and an alliance was made with the Christian kingdom of Kakhetia in Georgia in an attempt to offset Muslim influence in the area, but further inroads were repulsed by Daghestani and other mountain warriors.

From www.pbs.org

In a series of strategic moves after the fall of Astrakhan in 1556, Russia attempted to annex first the western, then the central, and finally the eastern Caucusus. A variety of strategies were used: outright military conquest, co-option, colonial settlement, and forced Christianization.

From Christians associated for relations in Eastern Europe

Prior to the mid-sixteenth century, Russia had no significant contacts with the peoples of the North Caucasus. The situation changed as a result of Ivan the Terrible's conquest of the khanate of Astrakhan, at the mouth of the Volga River, in 1556. Russia was now a Caspian power and became involved in the conflicts of the North Caucasus. In 1562 the tsar Ivan sent a five hundred men force accompanied by an equal number of Cossack settlers. More parties of Cossacks continued to settle along the lower course of the Terek River and on the foothills of Chechnia. These Cossack communities were composed of runaway serfs, soldiers of fortune, religious dissenters, and those Cossacks whose territories in the Ukraine and along the lower Volga had been absorbed into the expanding Russian state. These Cossack settlers subsequently became known as the Terek Cossacks.

From www.aternativesjournal.com

Taurida, or the Crimea, was Russia’s indeed. However, the poet was premature in hailing the end of the conquest of the Caucasus. His poem and music composed by Joseph Kozlovsky became Russian national anthem in 1791. The Caucasus, however, was still not conquered. In 1817, when General Alexey Yermolov returned victorious from Persia, the war of conquest began. In 1818, the general founded the Groznaya fortress on Sunja River. Ivan the Terrible issued the first order to build a fortress in this particular place immediately after he subjugated Kazan and Astrakhan in the 16th century. Yermolov executed the czar’s order and named the fortress after him (“grozny” means “terrible” in Russian). After the fortress was founded, the main line of defense was moved from the Terek River to the Sunja River. It was believed that within a few years the people who lived in the mountains where Noah’s Arc landed would happily join Russia.

From www.military-en.rian.ru

...just in case you were interested in the history of your nation.

Breaking my promise...
What you want to prove is that Russia long time ago had an eye on Chechens and all that time was pursuing the goal to harm them. Questionable assumption.
Astrakhan hardly can be called a Cuacasian city. With all due respect to your sources, it still 400 kilometers away from Grozny (which is in the northern part of Chechnya, i.e. Northern Caucasses).
I know how it feels. From London it looks like Chicago and San Francisco are quite close to each other. Or Moscow is nearly at the foothills of Ural mountains.
:)
In the middle of 16th century Russian Empire was fighting with Turks and Persians on the South, Swedes on the North-West, Tatars on the South-West and East. It was "do or die" situation. Daghestani warroiors (sure, they were warriors, Russians were just barbarious intruders :) were in fact armed and sponsored by Persians, being a mere tool in the war.
So, according to the rules of fuzzy logic, Kazan was the key to Caucasses, in the very same way as Narva (building Ivan-gorod fortress) layed a way for conquering Cacasses.
Still not accepting your point (Kazan-Caucasses connection).

Let us just put our hands on our hearts... The same can be said about Poland - how it tried to invade Russia in 1612, 1812, 1918-1924. (Which would put "rightful" suspicion - why exactly there were trying to do so?). However I am sane enough NOT to put it that way, since I believe that these artificial historical parallels are taken out of context. I.e. I DO NOT believe that Poland and Poles are enemies and want to harm my country. What I do believe, that there is a huge amount of old prejudices and cliches which are cleared off of mothballs and put up into use to serve current political agendas.