Is there a commandment to love your parents?

Well its in the ten commandments so no its not just folk-religion. its also stated in Colossians 3:20 Children, obey your parents in all things for this is well pleasing unto the lord. Matthew 15:4 For God commanded, saying, Honour thy father and mother: and, He that curseth father or mother, let him die the death. or Exodus 20:1-17 “Honor your father and your mother, so that you may live long in the land the Lord your God is giving you.

What is "to love"?
"[To] love is to wish good to someone."¹

The LORD says,

"He who has my commandments and keeps them, he it is who loves me; and he who loves me will be loved by my Father, and I will love him and manifest myself to him.”²

And his Apostle to the Gentiles in his letter to the Romans writes³,

Love for One Another
8 Owe no one anything, except to love one another; for he who loves his neighbor has fulfilled the law. 9 The commandments, “You shall not commit adultery, You shall not kill, You shall not steal, You shall not covet,” and any other commandment, are summed up in this sentence, “You shall love your neighbor as yourself.” 10 Love does no wrong to a neighbor; therefore love is the fulfilling of the law.

Therefore to have God's commandments and keep them is to love God. And the proof that one loves their neighbor is in their keeping and not breaking the commandments that relate to neighbor. The first listed is,

“Honor your father and your mother, that your days may be long in the land which the Lord your God gives you."⁴

The "good" of father and mother from their children, established by God himself, is "honor" due to them.

Therefore honoring father and mother is loving father and mother and loving God [or at least not offending further] in keeping this commandment.

<sup>1. cf. Summa Theologica | New Advent > First Part of the Second Part > Question 26 > Article 4., Rom 15:1-3 (RSVCE) and CCC 1766 "To love is to will the good of another." All other affections have their source in this first movement of the human heart toward the good. Only the good can be loved. Passions "are evil if love is evil and good if it is good.". Please read also the entire Article 5 CCC 1762-1775.
2. cf John 14:21 (RSVCE).
3. cf. Rom 13:8-10 (RSVCE).
4. cf. Exod (RSVCE).</sup>

In this context, it seems clear that "honor your parents" includes "love". But that does not imply, necessarily, feelings of affection. Jesus sharp words to the Pharisees about this commandment is instructive (Matt 15:3-6), and it focus on the "wealth" meaning of the Hebrew word. "But you say that if anyone declares that what might have been used to help their father or mother is ‘devoted to God,' they are not to ‘honor their father or mother’ with it."

He is clearly talking about money or goods, not feelings of affection. This meaning is also captured in the English word "honorarium", which is money paid to someone honorable (for their service).

Jesus as Rabbi is opposed to the Pharisee teaching and says clearly that honoring father and mother includes, at least, providing for their material needs. Doing so is loving with actions (1 John 3:18). We clearly have the responsibility to love "our neighbor" (presumably including parents), and further with relatives to provide for them (1 Tim 5:8).

Yes. We are commanded to love even our enemies, and specifically to care for our parents. This is a primary way in which we put our faith into practice, and people who neglect their parents cannot persist in the faith. In 1 Timothy 5:3-8, Paul is instructing a young pastor in caring for elderly widows in the Church.

Give proper recognition to those widows who are really in need. But if a widow has children or grandchildren, these should learn first of all to put their religion into practice by caring for their own family and so repaying their parents and grandparents, for this is pleasing to God. The widow who is really in need and left all alone puts her hope in God and continues night and day to pray and to ask God for help. But the widow who lives for pleasure is dead even while she lives. Give the people these instructions, so that no one may be open to blame. Anyone who does not provide for their relatives, and especially for their own household, has denied the faith and is worse than an unbeliever.